Caracterização do nível crítico para as soluções de energia mínima de uma classe de problemas elípticos semi-lineares

Abstract

The least energy solutions are de ned as solutions that indicate infi mum value to the energy functional image associated with a class of nonlinear variational problems −∆u = g(u) u ∈ H1(RN) The objective of this work is to show that through least energy solutions of nonlinear equation above, the Mountain pass value without the Palais Smale condition is critical point. For this, we will prove that under certain hypotheses on the function g and under a constraint assumption is possible to obtain a positive solution for the above problem, spherically symmetric and decreasing with the radius. Then the solution of the problem subject to this constraint has the lowest value in the energy functional among all solutions of the above problem applied in the same functional. In this context, it guarantee the existence of at least one solution of the least energy. The above results were obtained in [2] and [1]. Key Words: Least Energy, Mountain Pass, Minimization, Minimum of the Action.