The Existence And Concentration Phenomenon Of Sign-changing Solutions To Two Classes Of Nonlocal Elliptic Equations

The existence and concentration of sign-changing solutions of nonlinear elliptic equa-tions is a hot topic in the field of nonlinear analysis.In this thesis,we study the existence of sign-changing solutions of the Kirchhoff equations and the fractional Schrodinger equations via variational methods.Moreover,we study the concentration behavior of sign-changing solutions of Kirchhoff equations.Firstly,we introduce the background and some recen-t works of the Kirchhoff equations and the fractional Schrodinger equations,and some conclusions will be used later.Secondly,the multiplicity and concentration phenomena of solutions of a class of Kichhoff equations are studied via the variational methods.We showed,for any given positive integer k,the existence of k pairs of solutions are obtained,and these solutions concentrate around the local minimum of the potential if the parameter small enough.Thirdly,we study a class of fractional Schrodinger equations with critical exponent.We showed,for any given positive integer k,the existence of k pairs of solutions are obtained.