| In this thesis,we are concerned with Kirchhoff-Schr(?)dinger-Poisson system.By using the method of invariant sets of descending flow and abstract critical point theory,we show the existence and multiplicity of sign-changing solutions to Kirchhoff-Schr(?)dingerPoisson systems.This thesis is organized as follows:In Chapter 1,we introduce the background,significance and current status of our problems.Meanwhile,the main results of this thesis are presented.In Chapter 2,we briefly introduce some definitions,notations and preliminary knowledge of this thesis.In Chapter 3,we consider the following Kirchhoff-Schr(?)dinger-Poisson system:with a,b>0.We show the existence and multiplicity of sign-changing solutions when f satisfies the(AR)condition with μ>4.This result extends the result in reference[46]to Kirchhoff-Schr(?)dinger-Poisson system.In addition,we also give the special case that the above system has only zero solution when μ<4.In Chapter 4,we consider the following Kirchhoff-Schr(?)dinger-Poisson system:with a,b>0,p ∈(4.5,6).We show the existence and multiplicity of sign-changing solutions to this system.In particular,the Ambrosetti-Rabinowitz condition is not required.In Chapter 5,we consider the following Kirchhoff-Schr(?)dinger-Poisson system:with a,b>0,p ∈(4.5,6).We show the existence and multiplicity of sign-changing solutions when the corresponding conditions are satisfied.In Chapter 6,we summarize and prospect the whole thesis. |
