Ground State Solutions And Multiple Positive Solutions For Nonhomogeneous Schr(?)dinger Equations And Schr(?)dinger-Poisson System

In this paper,we study the existence of ground state solutions and multiple pos-itive solutions for nonhomogeneous Schr(?)dinger equations and Schr(?)dinger -Poisson system.The paper is divided into five chapters,the main contents are as follows:Chapter One mainly introduces the physical background,the current situation and the latest progress of the research,and then makes a brief introduction to the work of this paper,and gives some necessary basic symbols and important theorems.In chapter two,we consider a class of nonhomogeneous Schr(?)dinger equations-△u=g(u)+h(x),x∈RN,(0.0.1)where N≥3,g is a continuous function and h(x)(?)0.On the basis of variational methods,by using Ekeland’s variational principle and a Pohozaev type identity,we obtain the existence of ground state solutions when |h|2 is small enough.In chapter three,we continue to discuss equation(0.0.1),where N≥ 3,h(x)(?)0 and g satisfies the conditions of Berestycki-Lions type.Similarly,on the basis of vari-ational methods,by using Ekeland’s variational principle,the mountain pass theo-rem and a Pohozaev type identity,we obtain the existence of two positive solutions under the suitable assumptions on h.In chapter four,we study the nonhomogeneous Schr(?)dinger -Poisson system where λ>0 is a parameter,h(x)(?)0.Under the Berestycki-Lions type conditions on g,we prove that there exists λ0>0 such that the system has at least two positive radial solutions for λ∈(0,λ0)by using variational methodsIn chapter five,we give some analysis and consideration according to the results of this paper.