Existence and asymptotic behavior of solutions for nonlinear Schrödinger-Poisson systems with steep potential well

摘要

In this paper, we are concerned with a class of Schrödinger-Poisson systems with the asymptotically linear or asymptotically 3-linear nonlinearity. Under some suitable assumptions on V, K, a, and f, we prove the existence, nonexistence, and asymptotic behavior of solutions via variational methods. In particular, the potential V is allowed to be sign-changing for the asymptotically linear case.