An existence theorem for the Boltzmann Equation with force term and small initial data is proved in an L 1 setting.

By applying a nonlinear alternative of Leray-Schauder type, a fixed point of an operator is found, which, in turn, comes to be a solution of stationary Boltzmann equation with boundary conditions of Maxwellian type. RESUMENAplicando una alternativa no lineal del tipo Leray-Schauder, se encontró un punto fijo de un operador, el cual corresponde a la solución de una ecuación de Boltzmann estacionaria con condiciones de frontera del tipo Maxwelliano.

La meta en este paper es probar existencia y unicidad de soluciones para la ecuación de Enskog con término fuerza The goal in this paper is prove existence and uniqueness of solutions for the Enskog equation with force term.

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 J’’0(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.