A Study On The Existence Of Sign-changing Solutions For Two Fractional-order Elliptic Equations

In this paper,we apply variational methods to study two fractional nonlocal elliptic equations.The existence of ground state and sign-changing solutions are discussed respectively.In Chapter 1,we briefly describe the research background,research status,mark,basic definition and main research results of this paper.In Chapter 2,we study the existence of sign-changing solutions for a class of fractional Kirchhoff-Poisson system.By using the Nehari manifold method and the deformation lemma,we prove that there are sign-changing ground state solutions for the system when the potential and nonlinear terms meet the certain conditions.In Chapter 3,we study the existence of ground state solutions for a class of fractional Schrodinger-Poisson system with critical growth and vanishing potentials.By using the mountain pass theorem and the Nehari manifold method,we prove that the system has positive and sign-changing ground state solutions when the potential and nonlinear terms meet the certain conditions.