Existence of nontrivial solution for a 4-sublinear Schrödinger–Poisson system

• DOI: 10.1016/j.aml.2014.07.017
• Publication Date: 2014-07-28T15:05:11Z
• Authors: Shaowei Chen; Dawei Zhang
• Keywords: Sublinear function; Sequence (biology); Schrödinger's cat

Abstract We consider a Schrodinger–Poisson system in R 3 with potential indefinite in sign and a general 4-sublinear nonlinearity. Its variational functional does not satisfy the Palais–Smale condition in general. We use a finite-dimensional approximation method to obtain a sequence of approximate solutions. Then we prove that these approximate solutions converge weakly to a nontrivial solution of this system.