Um teorema de linking abstrato aplicado a uma equação assintoticamente linear

Abstract

In this work, we present an abstract linking theorem for Cerami sequences, but without using the Cerami condition. This theorem will be used to obtain nontrivial solution to indefinite problems. We will apply the mentioned theorem to obtain a nontrivial solution for the Schrödinger equation, −∆u + V (x)u = g(x, u), where g(x, s) = h(x)f(s), wherein the nonlinearity f is asymptotically linear and V is a very general potential. By applying this result, a critical point of a functional associated with the problem will be obtained. This critical point will be a weak solution to the problem. Spectral theory will be a fundamental tool for obtaining a linking structure to the functional associated with the mentioned problem.