Resumen de Existence and Multiplicity of Solutions for a Fractional Schrödinger–Poisson System with Subcritical or Critical Growth

Guangze Gu, Changyang Mu, Zhipeng Yang

• In this paper, we study the existence of positive ground state solutions and infinitely many geometrically distinct solutions for the following fractional Schrödinger– Poisson system (−)su + V(x)u + φu = f (x, u), in R3, (−)sφ = u2, in R3, where s ∈ ( 3 4 , 1) is a fixed constant, f is continuous, superlinear at infinity with subcritical or critical growth and V and f are asymptotically periodic in x. Applying the method of Nehari manifold and Lusternik–Schnirelmann category theory, three existence results are given.