Existence of solution for a class of Schrödinger-Poisson type system without the Ambrosetti-Rabinowitz condition
Elliptic partial differential equations; Schrödinger-Poisson systems; Variational methods; Nehari manifold
In this work we study the existence of stationary solutions to a problem involving Schrödinger-Poisson type systems. We are interested in obtaining minimum energy solutions using the theory of variational methods applied to nonlinear partial differential equations. The nonlinearities present in our problem do not satisfy the Ambrosetti-Rabinowitz condition, which makes the analysis of Palais-Smale sequences more involved. In particular, to achieve our goals, it is of fundamental importance to use the Mountain Pass Theorem, the Compactness Concentration Lemma and the Nehari manifold method.