Nontrivial solutions for the fractional Schrödinger‐Poisson system with subcritical or critical nonlinearities

Abstract

In this paper, we are concerned with a class of fractional Schrödinger-Poisson system involving subcritical or critical nonlinearities. By using the Nehari manifold and variational methods, we obtain the existence and multiplicity of nontrivial solutions. KEYWORDS critical Sobolev exponents, fractional Schrödinger-Poisson system, Nehari manifold, variational methods MSC CLASSIFICATION 35A15; 35J60; 35R11; 35R09 { −Δu + V(x)u + (x)u = (x, u), x ∈ R 3 , −Δ = u 2 , x ∈ R 3 .