Existence of solutions to a class of Schrödinger–Poisson systems with indefinite nonlinearity. Issue 5 (4th April 2017) - Li, Fuyi; Chang, Caihong; Feng, Xiaojing
Abstract : In this paper, we investigate a class of Schrödinger–Poisson systems with indefinite nonlinearity which is a combination of a linear term with parameter and a superlinear term with parameter . Here, the Poisson equation is the form, where . A concentration compactness lemma is established to overcome the lack of compactness. In order to insure the Nehari manifold, the parameters and must have some restriction that compares with and the variation range of depends on l . By seeking the local minimizer of the energy functional on the Nehari manifold, we obtain the existence of solution for the system.