Ground state solutions for asymptotically periodic Schrödinger-Poisson systems in R^2

Abstract

<p>This article concerns the planar Schrödinger-Poisson system</p> <pre>-∆u + V(x)u + φu = ƒ(x, u), x ∈ ℝ²,<br> ∆φ = u², x ∈ ℝ²,</pre> <p>where V(x) and ƒ(x, u) are periodic or asymptotically periodic in x. By combining the variational approach, the non-Nehari manifold approach and new analytic techniques, we establish the existence of ground state solutions for the above problem in the periodic and asymptotically periodic cases. In particular, in our study, ƒ is not required to satisfy the Ambrosetti-Rabinowitz type condition or the Nehari-type monotonic condition.</p>