We consider a Schrödinger-Poisson system in with a strongly indefinite potential and a general nonlinearity. Its variational functional does not satisfy the global linking geometry. We obtain a nontrivial solution and, in case of odd nonlinearity, infinitely many solutions using the local linking and improved fountain theorems, respectively.
"Existence of Multiple Nontrivial Solutions for a Strongly Indefinite Schrödinger-Poisson System." Abstr. Appl. Anal. 2014 1 - 8, 2014. https://doi.org/10.1155/2014/240208