Ecuaciones semilineales con espectro discreto

Este libro está diseñado como un primer curso sobre ecuaciones diferenciales semilineales para estudiantes con conocimientos básicos de álgebra lineal, análisis matemático y ecuaciones diferenciales. El estudio del primer capítulo solamente requiere de conocimientos básicos de ecuaciones diferencial...

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Autores:
Caicedo Contreras, José Francisco
Castro, Alfonso
Tipo de recurso:
Book
Fecha de publicación:
2012
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
spa
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oai:repositorio.unal.edu.co:unal/79984
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https://repositorio.unal.edu.co/handle/unal/79984
https://repositorio.unal.edu.co/
Palabra clave:
510 - Matemáticas::515 - Análisis
Ecuaciones diferenciales parciales
Ecuaciones diferenciales semilineales
Teoría espectral
Análisis funcional
Funciones de Green
Ecuaciones
Rights
openAccess
License
Atribución-NoComercial-SinDerivadas 4.0 Internacional
id UNACIONAL2_ded1d954b36f344a1acf611e9f647877
oai_identifier_str oai:repositorio.unal.edu.co:unal/79984
network_acronym_str UNACIONAL2
network_name_str Universidad Nacional de Colombia
repository_id_str
dc.title.spa.fl_str_mv Ecuaciones semilineales con espectro discreto
title Ecuaciones semilineales con espectro discreto
spellingShingle Ecuaciones semilineales con espectro discreto
510 - Matemáticas::515 - Análisis
Ecuaciones diferenciales parciales
Ecuaciones diferenciales semilineales
Teoría espectral
Análisis funcional
Funciones de Green
Ecuaciones
title_short Ecuaciones semilineales con espectro discreto
title_full Ecuaciones semilineales con espectro discreto
title_fullStr Ecuaciones semilineales con espectro discreto
title_full_unstemmed Ecuaciones semilineales con espectro discreto
title_sort Ecuaciones semilineales con espectro discreto
dc.creator.fl_str_mv Caicedo Contreras, José Francisco
Castro, Alfonso
dc.contributor.author.none.fl_str_mv Caicedo Contreras, José Francisco
Castro, Alfonso
dc.contributor.illustrator.none.fl_str_mv Rubiano, Gustavo
dc.subject.ddc.spa.fl_str_mv 510 - Matemáticas::515 - Análisis
topic 510 - Matemáticas::515 - Análisis
Ecuaciones diferenciales parciales
Ecuaciones diferenciales semilineales
Teoría espectral
Análisis funcional
Funciones de Green
Ecuaciones
dc.subject.lemb.spa.fl_str_mv Ecuaciones diferenciales parciales
Ecuaciones diferenciales semilineales
Teoría espectral
dc.subject.proposal.spa.fl_str_mv Análisis funcional
Funciones de Green
Ecuaciones
description Este libro está diseñado como un primer curso sobre ecuaciones diferenciales semilineales para estudiantes con conocimientos básicos de álgebra lineal, análisis matemático y ecuaciones diferenciales. El estudio del primer capítulo solamente requiere de conocimientos básicos de ecuaciones diferenciales elementales. Para el segundo capítulo se necesita manejo de las coordenadas polares y el teorema del valor intermedio. Lo anterior, más conocimiento de ecuaciones diferenciales ordinarias singulares facilitan el estudio del capítulo 3. En el capítulo métodos de orden, se usa a menudo el papel de las segundas derivadas parciales por su importancia para determinar mínimos o máximos locales. El estudio de los capítulos 5 a 8 requiere de cierta familiaridad con conceptos básicos del análisis funcional tales como la integral de Lebesgue, espacios de Hilbert y espacios Lp. (Texto tomado de la fuente).
publishDate 2012
dc.date.issued.none.fl_str_mv 2012
dc.date.accessioned.none.fl_str_mv 2021-08-20T17:38:01Z
dc.date.available.none.fl_str_mv 2021-08-20T17:38:01Z
dc.type.spa.fl_str_mv Libro
dc.type.driver.spa.fl_str_mv info:eu-repo/semantics/book
dc.type.version.spa.fl_str_mv info:eu-repo/semantics/acceptedVersion
dc.type.coar.spa.fl_str_mv http://purl.org/coar/resource_type/c_2f33
dc.type.content.spa.fl_str_mv Text
dc.type.redcol.spa.fl_str_mv http://purl.org/redcol/resource_type/LIB
format http://purl.org/coar/resource_type/c_2f33
status_str acceptedVersion
dc.identifier.uri.none.fl_str_mv https://repositorio.unal.edu.co/handle/unal/79984
dc.identifier.instname.spa.fl_str_mv Universidad Nacional de Colombia
dc.identifier.reponame.spa.fl_str_mv Repositorio Institucional Universidad Nacional de Colombia
dc.identifier.repourl.spa.fl_str_mv https://repositorio.unal.edu.co/
url https://repositorio.unal.edu.co/handle/unal/79984
https://repositorio.unal.edu.co/
identifier_str_mv Universidad Nacional de Colombia
Repositorio Institucional Universidad Nacional de Colombia
dc.language.iso.spa.fl_str_mv spa
language spa
dc.relation.ispartofseries.none.fl_str_mv Colección textos;
dc.relation.citationedition.spa.fl_str_mv Primera edición
dc.relation.references.spa.fl_str_mv R. Adams, Sobolev spaces, Academic Press, New York, 1975.
I. Ali and A. Castro, Positive solutions for a semilinear elliptic problem with critical exponent, Nonlinear Analysis 27 (1996), no. 3, 327– 338.
J. Ali, R. Shivaji, and M. Ramaswamy, Multiple positive solutions for classes of elliptic systems with combined nonlinear effects, Differential Integral Equations 19 (2006), no. 6, 669–680.
H. Amann, Fixed point problems and nonlinear eigenvalue problems in ordered Banach spaces, SIAM Review 18 (1976), 620–709.
Saddle points and multiple solutions of differential equations, Math. Z. (1979), 127–166.
H. Amann and S. A. Weiss, On the uniqueness of the topological degree, Math. Z. 130 (1973), 39–54.
P. Bates and A. Castro, Existence and uniqueness for a variational hyperbolic systems, Nonlinear Analysis. 4 (1980), no. 6, 1151–1156.
Necessary and sufficient conditions for existence of solutions to equations with noninvertible linear part, Rev. Colombiana.Mat. 15 (1981), no. 1, 7–23.
V. Benci and D. Fortunato, Towards a unified field theory for classical electrodynamics, Arch. Ration. Mech. Anal. 173 (2004), no. 3, 379–414.
V. Benci and P. Rabinowitz, Critical point theorems for indefinite functionals, Inventions math. 52 (1979), 241–273.
A.G. Bratsos, the solution of the two dimensional sine-gordon equation using the method of lines, Journal of Computational and Applied Mathematics 206 (2007), 251–277.
H. Brezis, Analyse Fonctionelle, Masson, 1983.
H. Brezis and L. Nirenberg, Characterizations of the ranges of some nonlinear operators and applications to boundary value problems, Annali della Scuola Norm. Sup. di Pisa (1978), 225–236.
R. Brooks and K. Schmitt, The contraction mapping principle and some applications, Electronic Journal of Differential Equations, Monograph (2009), 225–236.
J. Caicedo and A. Castro, A semilinear wave equation with derivative of nonlinearity containing multiple eigenvalues of infinite multiplicity, Contemp. Math. 208 (1997), 111–132.
J.F. Caicedo and A. Castro, A semilinear wave equation with smooth data and no resonance having no continuous solution, Discrete and Continuous Dynamical Systems 24 (2009), 653–658.
J.F. Caicedo, A. Castro, and R. Duque, Existence of solutions for a wave equation with nonmonotone nonlinearity and a small parameter, preprint (2010).
R. Cantrell, C. Cosner, and S. Martínez, Global bifurcation of solutions to diffusive logistic equations on bounded domains subject to nonlinear boundary conditions, Proc. Roy. Soc. Edinburgh Sect. A 139 (2009), no. 1, 45.
A. Castro, Sufficient conditions for the existence of weak solutions of the boundary value problem Lu=g(u(x ),x ) (x ∈ Ω), u(x )=0 (x ∈ ∂Ω), Rev. Colombiana Mat. (1975), no. 3, 173–187.
Hammerstein integral equations with indefinite kernel, Internet. J. Math. Sci. 1 (1978), no. 8, 187–201.
Periodic solutions of the forced pendulum equation, Academic Press (1980), 149–160.
A. Castro, J. Cossio, and J.M. Neuberger, A sign changing for a superlinear Dirichlet problem, Rocky Mountain J.Math.
A minimax principle, index of the critical point, and existence of sign changing solutions to elliptic boundary value problem, Electron. J. Differential Equations 02 (1998), 18.
A. Castro, J. Cossio, and C.A. Velez, Existence of seven solutions for an asymptotically linear Dirichlet problem, preprint (2010).
A. Castro and A. Kurepa, Energy analysis of a nonlinear singular diferencial equation and applications, Rev. Colombiana Mat. 21 (1987), 155–166.
A. Castro and A. Lazer, Applications of a maximun principle, Rev.Col. de Mat. (1976).
Critical point theory and the numbers of solutions of a nonlinear dirichlet problem, Ann. Mat. Pura Appl. 4 (1979), no. 120.
On periodic solutions of weakly coupled systems of differential equations, Boll. Un. Mat. Ital. B 5 (1981), no. 18, 733–742.
A. Castro and B. Preskill, Existence of solutions for a semilinear wave equation with non-monotone nonlinearity, Discrete Contin. Dyn. Syst. 28 (2010), no. 2, 649.
A. Castro and R. Shivaji, Non-negative solutions for a class of nonpositone problems, Proc. Royal Soc. Endinburg Sect. A 108 (1988), no. 8, 291–302.
Non-negative solutions to a semilinear Dirichlet problem in a ball are positive and radially symmetric, Comm. in Partial Differential Equations 14 (1989), no. 8, 1091–1100.
A. Castro and S. Unsurangsie, A semilinear wave equation with non-monotone nonlinearity, Pacific J. Math 132 (1988), no. 2, 215–225.
S. Cingolani and M. Clapp, intertwining semiclassical bound states to a nonlinear magnetic schrodinger equation, Nonlinearity 22 (2009), no. 9, 2309–2331.
Symmetric semiclassical states to a magnetic nonlinear schrodinger equation via equivariant morse theory, Commun. Pure Appl. Anal. 9 (2010), no. 5, 1263–1281.
D. Clark, A variant of the Lusternik-Schnierelmann theory, Indiana Univ. Math. J. 22 (1972), 579–584.
D. de Figueiredo, P. Lions, and R. Nusbaum, A priori and existence of positive solutions of semilinear elliptic equations, J. Math. Pures. Appl. 61 (1982), 41–63.
P. Drabek, A. Kufner, and F. Nicolosi, Quasilinear elliptic equations with degenerations and singularities, Walter de Gruyter, Berlin, New York, 1997.
S. Fucik, J. Necas, J. Soucek, and V. Soucek, Spectral analysis of nonlinear operators, vol. 343, Springer Verlag, 1973.
B. Gidas, W. Ni, and L. Nirenberg, Symmetry and related properties via the maximum principle, Comm. Math. Phys. 68 (1979), 209–243.
B. Gidas and J. Spruck, A priori bounds for positive solutions of nonlinear elliptic equations, Comm. Partial Differential Equations. 6 (1981), 883–901.
D. Gilbarg and N.S. Trudinger, Elliptic partial differential equations of second order, Springer-Verlag, 1998.
V. Guillemin and A. Pollack, Differential Topology, Prentice Hall, Inc, 1974.
H. Hofer, On the range of a wave operator with non-monotone nonlinearity, Math. Nachr. 106 (1982), 327–340.
J. Jacobsen and K. Schmitt, Radial solutions of quasilinear elliptic differential equations, Elsevier/North-Holland.
J. Jia and J. Huang, Krylov deferred correction accelerated method of lines transpose for parabolic problems, Journal of computational Physics 227 (2008), 1739–1753.
D. Joseph and T. Lundgren, Quasilinear Dirichlet problems driven by positive sources, Arch. Rational Mech. Anal. 49 (1973), 241–269.
A. Khamayseh and R. Shivaji, Evolution of bifurcation curves for semipositone problems when nonlinearities develop multiple zeroes, Appl. Math. Comput. 52 (1992), no. 2, 173–188.
M. Krasnoselskii, Topological methods in the theory of nonlinear integral equations, Pergamon Press, London, New York, 1964.
E. Landesman and A. Lazer, Nonlinear perturbations of elliptic boundary value problems at resonance, J. Math. Mech. 19 (1970).
S. Lang, Real Analysis, Addisson-Wesley Publishing Company, 1983.
A. Lazer, E. Landesman, and D. Meyers, On saddle point problems in the calculus of variations, the ritz algorithm, and monotone convergence, J. Math. Appl. 52 (1975), no. 3.
N.G. Lloyd, Degree theory, Cambridge University Press., 1978.
J. Mawhin, Periodic solutions of some semilinear wave equations and systems: a survey, Chaos, Solitons, and Fractals 5 (1995), 1651– 1669.
P. J. McKenna, On solutions of a nonlinear wave equation when the ratio of the period to the length of the interval is irrational, Proc. Amer. Math. Soc. 93 (1985), no. 1, 59–64.
A. Miciano and R. Shivaji, Multiple positive solutions for a class of semipositone Newmann two boundary value problems, J. Math. Anal. Appl. 178 (1993), no. 1, 102–115.
J. Milnor, Topology from a differentiable viewpoint, Princeton University Press.
L. Nirenberg, Topics in nonlinear functional analysis, Courant Institute Lecture Notes, New York, 1974.
F. Pacella and T. Weth, Symmetry of solutions to semilinear elliptic equations via morse index, Proc. Amer. Math. Soc. 135, no. 6, 1753– 1762.
R. Palais, Lusternik-Schnirelmann theory on Banach manifolds, Topology 5 (1966), 115–132.
M. Protter and H. Weinberger, Maximun principles in differential equations, Prentice Hall, Englewood, Cliffs, N.J., 1967.
P. Pucci and J. Serrin, A general variational identity, Indiana Univ. Math. J. 35 (1986), 681–703.
P.H. Rabinowitz, Some global results for nonlinear eigenvalue problems, J. Funct. Anal. 7 (1971), 487–513.
Periodic solutions of Hamiltonian systems, Com. Pure Appl. Math. 31 (1978), 157–184.
Some minimax theorems and applications to nonlinear partial differential equations, Nonlinear Analysis, Ac.Press 65 (1978), 161–177.
Minimax methods in critical point theory with applications to differential equations, CBMS 65 (1985).
M. Reed and B. Simon, Methods of modern mathematical physics, Academic Press., Inc., 1980.
H. Royden, Real Analysis, McMillan Publishing Co., Inc., 1968.
W. Rudin, Principles of mathematical analysis, McGraw-Hill, New York, 1976.
Real and complex analysis, McGraw-Hill, New York, 1987.
J. Schwartz, Nonlinear functional analysis, Gordon Breach, New York, 1962.
M. Willem, Density of the range of potential operators, Proc. Amer. Math. Soc. 83 (1981), no. 2, 341–344.
P. Zhao, C. Zhong, and J. Zhu, Positive solutions for a nonhomogeneous semilinear elliptic problem with supercritical exponent, J. Math. Anal. Appl. 254 (2001), no. 2, 335–347.
dc.rights.spa.fl_str_mv Derechos Reservados al Autor, 2012
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.license.spa.fl_str_mv Atribución-NoComercial-SinDerivadas 4.0 Internacional
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rights_invalid_str_mv Atribución-NoComercial-SinDerivadas 4.0 Internacional
Derechos Reservados al Autor, 2012
http://creativecommons.org/licenses/by-nc-nd/4.0/
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eu_rights_str_mv openAccess
dc.format.extent.spa.fl_str_mv xiii, 175 páginas
dc.format.mimetype.spa.fl_str_mv application/pdf
dc.publisher.spa.fl_str_mv Universidad Nacional de Colombia
dc.publisher.department.spa.fl_str_mv Sede Bogotá
dc.publisher.place.spa.fl_str_mv Bogotá, Colombia
institution Universidad Nacional de Colombia
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spelling Atribución-NoComercial-SinDerivadas 4.0 InternacionalDerechos Reservados al Autor, 2012http://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Caicedo Contreras, José Francisco4131f0c3687f4a4a988d11938f9a1a46Castro, Alfonsoa25d5bc00937596a1d1f831ecebc03bbRubiano, Gustavo2021-08-20T17:38:01Z2021-08-20T17:38:01Z2012https://repositorio.unal.edu.co/handle/unal/79984Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/Este libro está diseñado como un primer curso sobre ecuaciones diferenciales semilineales para estudiantes con conocimientos básicos de álgebra lineal, análisis matemático y ecuaciones diferenciales. El estudio del primer capítulo solamente requiere de conocimientos básicos de ecuaciones diferenciales elementales. Para el segundo capítulo se necesita manejo de las coordenadas polares y el teorema del valor intermedio. Lo anterior, más conocimiento de ecuaciones diferenciales ordinarias singulares facilitan el estudio del capítulo 3. En el capítulo métodos de orden, se usa a menudo el papel de las segundas derivadas parciales por su importancia para determinar mínimos o máximos locales. El estudio de los capítulos 5 a 8 requiere de cierta familiaridad con conceptos básicos del análisis funcional tales como la integral de Lebesgue, espacios de Hilbert y espacios Lp. (Texto tomado de la fuente).Incluye índice analítico.ISBN de la versión impresa 9789587612424Primera ediciónxiii, 175 páginasapplication/pdfspaUniversidad Nacional de ColombiaSede BogotáBogotá, ColombiaColección textos;Primera ediciónR. Adams, Sobolev spaces, Academic Press, New York, 1975.I. Ali and A. Castro, Positive solutions for a semilinear elliptic problem with critical exponent, Nonlinear Analysis 27 (1996), no. 3, 327– 338.J. Ali, R. Shivaji, and M. Ramaswamy, Multiple positive solutions for classes of elliptic systems with combined nonlinear effects, Differential Integral Equations 19 (2006), no. 6, 669–680.H. Amann, Fixed point problems and nonlinear eigenvalue problems in ordered Banach spaces, SIAM Review 18 (1976), 620–709.Saddle points and multiple solutions of differential equations, Math. Z. (1979), 127–166.H. Amann and S. A. Weiss, On the uniqueness of the topological degree, Math. Z. 130 (1973), 39–54.P. Bates and A. Castro, Existence and uniqueness for a variational hyperbolic systems, Nonlinear Analysis. 4 (1980), no. 6, 1151–1156.Necessary and sufficient conditions for existence of solutions to equations with noninvertible linear part, Rev. Colombiana.Mat. 15 (1981), no. 1, 7–23.V. Benci and D. Fortunato, Towards a unified field theory for classical electrodynamics, Arch. Ration. Mech. Anal. 173 (2004), no. 3, 379–414.V. Benci and P. Rabinowitz, Critical point theorems for indefinite functionals, Inventions math. 52 (1979), 241–273.A.G. Bratsos, the solution of the two dimensional sine-gordon equation using the method of lines, Journal of Computational and Applied Mathematics 206 (2007), 251–277.H. Brezis, Analyse Fonctionelle, Masson, 1983.H. Brezis and L. Nirenberg, Characterizations of the ranges of some nonlinear operators and applications to boundary value problems, Annali della Scuola Norm. Sup. di Pisa (1978), 225–236.R. Brooks and K. Schmitt, The contraction mapping principle and some applications, Electronic Journal of Differential Equations, Monograph (2009), 225–236.J. Caicedo and A. Castro, A semilinear wave equation with derivative of nonlinearity containing multiple eigenvalues of infinite multiplicity, Contemp. Math. 208 (1997), 111–132.J.F. Caicedo and A. Castro, A semilinear wave equation with smooth data and no resonance having no continuous solution, Discrete and Continuous Dynamical Systems 24 (2009), 653–658.J.F. Caicedo, A. Castro, and R. Duque, Existence of solutions for a wave equation with nonmonotone nonlinearity and a small parameter, preprint (2010).R. Cantrell, C. Cosner, and S. Martínez, Global bifurcation of solutions to diffusive logistic equations on bounded domains subject to nonlinear boundary conditions, Proc. Roy. Soc. Edinburgh Sect. A 139 (2009), no. 1, 45.A. Castro, Sufficient conditions for the existence of weak solutions of the boundary value problem Lu=g(u(x ),x ) (x ∈ Ω), u(x )=0 (x ∈ ∂Ω), Rev. Colombiana Mat. (1975), no. 3, 173–187.Hammerstein integral equations with indefinite kernel, Internet. J. Math. Sci. 1 (1978), no. 8, 187–201.Periodic solutions of the forced pendulum equation, Academic Press (1980), 149–160.A. Castro, J. Cossio, and J.M. Neuberger, A sign changing for a superlinear Dirichlet problem, Rocky Mountain J.Math.A minimax principle, index of the critical point, and existence of sign changing solutions to elliptic boundary value problem, Electron. J. Differential Equations 02 (1998), 18.A. Castro, J. Cossio, and C.A. Velez, Existence of seven solutions for an asymptotically linear Dirichlet problem, preprint (2010).A. Castro and A. Kurepa, Energy analysis of a nonlinear singular diferencial equation and applications, Rev. Colombiana Mat. 21 (1987), 155–166.A. Castro and A. Lazer, Applications of a maximun principle, Rev.Col. de Mat. (1976).Critical point theory and the numbers of solutions of a nonlinear dirichlet problem, Ann. Mat. Pura Appl. 4 (1979), no. 120.On periodic solutions of weakly coupled systems of differential equations, Boll. Un. Mat. Ital. B 5 (1981), no. 18, 733–742.A. Castro and B. Preskill, Existence of solutions for a semilinear wave equation with non-monotone nonlinearity, Discrete Contin. Dyn. Syst. 28 (2010), no. 2, 649.A. Castro and R. Shivaji, Non-negative solutions for a class of nonpositone problems, Proc. Royal Soc. Endinburg Sect. A 108 (1988), no. 8, 291–302.Non-negative solutions to a semilinear Dirichlet problem in a ball are positive and radially symmetric, Comm. in Partial Differential Equations 14 (1989), no. 8, 1091–1100.A. Castro and S. Unsurangsie, A semilinear wave equation with non-monotone nonlinearity, Pacific J. Math 132 (1988), no. 2, 215–225.S. Cingolani and M. Clapp, intertwining semiclassical bound states to a nonlinear magnetic schrodinger equation, Nonlinearity 22 (2009), no. 9, 2309–2331.Symmetric semiclassical states to a magnetic nonlinear schrodinger equation via equivariant morse theory, Commun. Pure Appl. Anal. 9 (2010), no. 5, 1263–1281.D. Clark, A variant of the Lusternik-Schnierelmann theory, Indiana Univ. Math. J. 22 (1972), 579–584.D. de Figueiredo, P. Lions, and R. Nusbaum, A priori and existence of positive solutions of semilinear elliptic equations, J. Math. Pures. Appl. 61 (1982), 41–63.P. Drabek, A. Kufner, and F. Nicolosi, Quasilinear elliptic equations with degenerations and singularities, Walter de Gruyter, Berlin, New York, 1997.S. Fucik, J. Necas, J. Soucek, and V. Soucek, Spectral analysis of nonlinear operators, vol. 343, Springer Verlag, 1973.B. Gidas, W. Ni, and L. Nirenberg, Symmetry and related properties via the maximum principle, Comm. Math. Phys. 68 (1979), 209–243.B. Gidas and J. Spruck, A priori bounds for positive solutions of nonlinear elliptic equations, Comm. Partial Differential Equations. 6 (1981), 883–901.D. Gilbarg and N.S. Trudinger, Elliptic partial differential equations of second order, Springer-Verlag, 1998.V. Guillemin and A. Pollack, Differential Topology, Prentice Hall, Inc, 1974.H. Hofer, On the range of a wave operator with non-monotone nonlinearity, Math. Nachr. 106 (1982), 327–340.J. Jacobsen and K. Schmitt, Radial solutions of quasilinear elliptic differential equations, Elsevier/North-Holland.J. Jia and J. Huang, Krylov deferred correction accelerated method of lines transpose for parabolic problems, Journal of computational Physics 227 (2008), 1739–1753.D. Joseph and T. Lundgren, Quasilinear Dirichlet problems driven by positive sources, Arch. Rational Mech. Anal. 49 (1973), 241–269.A. Khamayseh and R. Shivaji, Evolution of bifurcation curves for semipositone problems when nonlinearities develop multiple zeroes, Appl. Math. Comput. 52 (1992), no. 2, 173–188.M. Krasnoselskii, Topological methods in the theory of nonlinear integral equations, Pergamon Press, London, New York, 1964.E. Landesman and A. Lazer, Nonlinear perturbations of elliptic boundary value problems at resonance, J. Math. Mech. 19 (1970).S. Lang, Real Analysis, Addisson-Wesley Publishing Company, 1983.A. Lazer, E. Landesman, and D. Meyers, On saddle point problems in the calculus of variations, the ritz algorithm, and monotone convergence, J. Math. Appl. 52 (1975), no. 3.N.G. Lloyd, Degree theory, Cambridge University Press., 1978.J. Mawhin, Periodic solutions of some semilinear wave equations and systems: a survey, Chaos, Solitons, and Fractals 5 (1995), 1651– 1669.P. J. McKenna, On solutions of a nonlinear wave equation when the ratio of the period to the length of the interval is irrational, Proc. Amer. Math. Soc. 93 (1985), no. 1, 59–64.A. Miciano and R. Shivaji, Multiple positive solutions for a class of semipositone Newmann two boundary value problems, J. Math. Anal. Appl. 178 (1993), no. 1, 102–115.J. Milnor, Topology from a differentiable viewpoint, Princeton University Press.L. Nirenberg, Topics in nonlinear functional analysis, Courant Institute Lecture Notes, New York, 1974.F. Pacella and T. Weth, Symmetry of solutions to semilinear elliptic equations via morse index, Proc. Amer. Math. Soc. 135, no. 6, 1753– 1762.R. Palais, Lusternik-Schnirelmann theory on Banach manifolds, Topology 5 (1966), 115–132.M. Protter and H. Weinberger, Maximun principles in differential equations, Prentice Hall, Englewood, Cliffs, N.J., 1967.P. Pucci and J. Serrin, A general variational identity, Indiana Univ. Math. J. 35 (1986), 681–703.P.H. Rabinowitz, Some global results for nonlinear eigenvalue problems, J. Funct. Anal. 7 (1971), 487–513.Periodic solutions of Hamiltonian systems, Com. Pure Appl. Math. 31 (1978), 157–184.Some minimax theorems and applications to nonlinear partial differential equations, Nonlinear Analysis, Ac.Press 65 (1978), 161–177.Minimax methods in critical point theory with applications to differential equations, CBMS 65 (1985).M. Reed and B. Simon, Methods of modern mathematical physics, Academic Press., Inc., 1980.H. Royden, Real Analysis, McMillan Publishing Co., Inc., 1968.W. Rudin, Principles of mathematical analysis, McGraw-Hill, New York, 1976.Real and complex analysis, McGraw-Hill, New York, 1987.J. Schwartz, Nonlinear functional analysis, Gordon Breach, New York, 1962.M. Willem, Density of the range of potential operators, Proc. Amer. Math. Soc. 83 (1981), no. 2, 341–344.P. Zhao, C. Zhong, and J. Zhu, Positive solutions for a nonhomogeneous semilinear elliptic problem with supercritical exponent, J. Math. Anal. Appl. 254 (2001), no. 2, 335–347.510 - Matemáticas::515 - AnálisisEcuaciones diferenciales parcialesEcuaciones diferenciales semilinealesTeoría espectralAnálisis funcionalFunciones de GreenEcuacionesEcuaciones semilineales con espectro discretoLibroinfo:eu-repo/semantics/bookinfo:eu-repo/semantics/acceptedVersionhttp://purl.org/coar/resource_type/c_2f33Texthttp://purl.org/redcol/resource_type/LIBGeneralLICENSElicense.txtlicense.txttext/plain; charset=utf-83964https://repositorio.unal.edu.co/bitstream/unal/79984/1/license.txtcccfe52f796b7c63423298c2d3365fc6MD51ORIGINAL­Ecuaciones Semilineales con Espectro Discreto 9789587612424.pdf­Ecuaciones Semilineales con Espectro Discreto 9789587612424.pdfLibro del Departamento de Matemáticasapplication/pdf1490771https://repositorio.unal.edu.co/bitstream/unal/79984/2/%c2%adEcuaciones%20Semilineales%20con%20Espectro%20Discreto%209789587612424.pdfb22b389d506563d4dbc168d5bb5b608aMD52THUMBNAIL­Ecuaciones Semilineales con Espectro Discreto 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