Existence And Concentration Of Infinitely Many Sign-changing Solutions Of Semiclassical Schr(?)dinger-poisson Systems

In this thesis,we study the existence and concentration of sign-changing solutions for Schr(?)dinger-Poisson systems,by variational method,especially by the critical points theory.We obtain some new results.The organization of this thesis is as follows.In Chapter 1,the background and the latest research for all the investigated problems are introduced,some preliminaries and the main results are outlined.In Chapter 2,we study the following semiclassical Schr(?)dinger-Poisson system with critical nonlinearity#12 where ε>0 is a small parameter,λ,μ>0 are parameters,V:R3→R is bounded and the set of local minimum point of V is nonempty.We proved the existence of infinitely many sign-changing solutions by the method of invariant sets with descending flow and the truncation technique,and proved that these solutions are located near the local minimum point of the potential function V as ε→0 by the penalization method.In Chapter 3,we study the following semiclassical Schr(?)dinger-Poisson system(?) where ε>0 is a small parameter,λ>0 is a parameter and V:R3→R is a bounded potential function,the nonlinearity f is superlinear at the origin and at infinity,and is subcritical growth.We proved the existence of infinitely many sign-changing solutions by the method of invariant sets with descending flow and the truncation technique,and proved that these solutions are located near the local minimum point of the potential function V as ε→0 by the penalization method.