Existence and nonexistence of the ground state solutions for nonlinear Schrodinger equations with nonperiodic nonlinearities

摘要

In this paper we study the following nonlinear Schrodinger equation -Δu + a(x)u = f(x, u); u ∈ H~1 (R~N), where a is periodic with respect to x and f(x, u) is superlinear in u. Suppose that 0 lies in a gap of the spectrum σ(-Δ+a). Without periodic assumption on f, we prove the existence of ground state solution for the system. Moreover, we obtain some sufficient conditions for the nonexistence of ground state solution.