Existence Of Solutions For Two Types Of Fractional Schrödinger-Poisson Equations With Critical Exponential Growt

In this paper,we use topological and variational methods to study the existence,multiplicity and concentration of solutions of two kinds of fractional Schrodinger-Poisson systems with critical growth.In Chapter 1,we briefly describe the research background,research states,main research results,the mark and basic definitions of this paper.In Chapter 2,we study the fractional Schrodinger-Poisson system with doubly critical growth.By using the generalized Nehari manifold method,the Ljusternik-Schnirelmann theory and the Moser iteration argument,we prove the concentration of ground state solutions for the system when the potential satisfied the Ambrosetti-Rabinowitz condition.In Chapter 3,we study the fractional Schrodinger-Poisson system with critical frequency and critical growth.By using the global compactness lemma,the energy estimations and the Ljustemik-Schnirelmann theory,we prove that there are multiplicity of high energy solutions for the system.