Equações elípticas assintoticamente lineares com potencial que muda de sinal

Abstract

In this work, we consider Schrödinger's nonlinear equation, minus delta plus the potential of x times u equal to the function f of u.With u in space H one of Rn minus 0, where N is greater than or equal to 3, the potential is a non-periodic function that changes signs and f is an asymptotically linear function at infinity. In addition, the potential has a positive limit at infinity and the spectrum of the Schrödinger operator has a negative end. The existence of a weak solution is established using the spectral theory, the Linking theorem under the condition of Cerami and the iteration between translated solutions of the problem in the associated infinity.