Teoría de puntos críticos : Problemas semilineales elípticos.

Abstract

In the following work, the theory of critical points is studied to establish the existence of at least one weak solution for a superquadratic semilinear elliptic problem. After examining the theory of critical points, we have chosen to use the Mountain Pass Theorem to find the desired weak solution. First, certain properties will be defined that will be useful for solving the problem. Then, we will test the hypotheses required for the mountain pass theorem to hold. To prove these hypotheses, we must analyze the functional associated with our problem. Once we have all the hypotheses satisfied, we can conclude that our problem has at least one weak solution.