Bound and ground states for a class of Schrödinger–Poisson systems

Fubao Zhang, Li Cai
2019 Boundary Value Problems  
We are concerned with the following Schrödinger-Poisson system: Assuming that K(x) and a(x) are nonnegative functions satisfying and other suitable conditions, we show the existence of bound and ground states via a global compactness lemma and the Nehari manifold. Our result extends the existence result of positive solutions for Schrödinger-Poisson system with more than three times growth by Cerami and Vaira (J. Differ. Equ. 248:521-543, 2010) to the system with three times growth. MSC: 35J05;
more » ... rowth. MSC: 35J05; 35J50; 35J60
doi:10.1186/s13661-019-1238-5 fatcat:2cdslgcfebbv5dnrnjsxljrxnm