Nehari-type ground state positive solutions for superlinear asymptotically periodic Schrödinger equations (Q1724513)

Summary: We deal with the existence of Nehari-type ground state positive solutions for the nonlinear Schrödinger equation \(- \Delta u + V \left(x\right) u = f \left(x, u\right), x \in \mathbb{R}^N, u \in H^1 \left(\mathbb{R}^N\right)\). 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.