Nodal Bound State Of Nonlinear Problems Involving The Fractional Laplacian

This paper is concerned with the following nonlinear fractional Schrodinger problem?2s(-?)su+V(x)u=|u|p-2u,in RN where ?>0 is a small parameter,V(x)is a positive function,0<s<1 and 2<p<2N/N-2s(N>2s).Under some suitable conditions,for any positive integer k,we can construct a nonradial sign-changing solutions with exactly k maximum points and k minimum points near the local minimum point of V(x).This paper is divided into three chapters:In chapter 1,we introduce the background of the problem and main results of the thesis.In chapter 2,we will give some preliminaries and make an energy expansion for the functional corresponding to the problem.In chapter 3,we will carry out some basic estimates reduction procedure and prove the Theo-rem.