Nehari-Type Ground State Positive Solutions for Superlinear Asymptotically Periodic Schrödinger Equations

Abstract

We deal with the existence of Nehari-type ground state positive solutions for the nonlinear Schrödinger equation $-\mathrm{\Delta }u+V\left(x\right)u=f\left(x, u\right), x \in {\mathbb{R}}^N, u \in H^1 \left({\mathbb{R}}^N\right)$. Under a weaker Nehari condition, we establish some existence criteria to guarantee that the above problem has Nehari-type ground state solutions by using a more direct method in two cases: the periodic case and the asymptotically periodic case.