Stationary Boltzmann equation: an approach via Morse Theory (2021)
In this paper we study the unidimensional Stationary Boltzmann Equation by an approach via Morse theory. We define a functional J whose critical points coincide with the solutions of the Stationary Boltzmann Equation. By the calculation of Morse index of J00(0)h and the critical groups C2(J, 0) and C2(J,∞) we prove that J has two different critical points u1 and u2 different from 0, that is, solutions of Boltzmann Equation.