Positive ground states for integrodifferential Schrödinger–Poisson systems

This work is dedicated to the study of existence of solutions for a Schrödinger–Poisson type system involving possible different integrodifferential operators in the presence of a nonnegative but not bounded away from zero potential. We consider a pure power nonlinearity \(u \mapsto |u|^{p-2}u,\) $u\mapsto {|u|}^{p-2}u,$ with \(4-\beta<p<6/(3-2\alpha ),\) $4-\beta <p<6/(3-2\alpha ),$ where \(\alpha \) $\alpha$ and \(\beta \) $\beta$ are positive parameters described in each equation. Our argument is variational in nature and involves the use of a deformation type lemma on a minimization over a Nehari–Pohozaev manifold. Some regularity results are provided and a maximum type principle for integrodifferential operators is proved.