The Existence And Concentration Of Infinitely Sign-changing Solutions For Two Kinds Of Nonlocal Problems

In this thesis,we study the existence,multiplicity and concentration phenomenon of solutions for nonlocal elliptic type equation,by using the mothod of invariant sets of descending flow and the perturbation method.A series of new results are obtained as follows.In Chapter 1,we mainly introduce the physical background and the current research progress of the Choquard equation and the quasilinear Schrodinger-Poisson system,as well as the basic knowledge needed in this thesis.In Chapter 2,we consider the following semi-classical Choquard equation? where N?3,max{N-4,1}<?<N,2<p<N+?/N-2,?>0 is a small positive pa-rameter.Under suitable assumption for the potential function,the existence of infinitely sign-changing solutions to the above equation is obtained,and proved that these solutions concentrate around the critical point set of V.In Chapter 3,we study the following semi-classical quasilinear Schrodinger-Poisson system? where ?>0 is a small parameter,4<q<2·2*.Under suitable assumption for the potential function,the existence of infinitely sign-changing solutions to the above equation is obtained,and proved that these solutions concentrate around the critical point set of V.