Font Size: a A A

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

Posted on:2021-01-15Degree:MasterType:Thesis
Country:ChinaCandidate:L X HuangFull Text:PDF
GTID:2370330611964173Subject:Basic mathematics
Abstract/Summary:PDF Full Text Request
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 ?>0 is a parameter,h(x)(?)0.Under the Berestycki-Lions type conditions on g,we prove that there exists ?0>0 such that the system has at least two positive radial solutions for ??(0,?0)by using variational methodsIn chapter five,we give some analysis and consideration according to the results of this paper.
Keywords/Search Tags:Nonhomogeneous Schr(?)dinger equations, Ground sate solutions, Nonhomogeneous Schr(?)dinger-Poisson system, Positive solutons, Variational method, Berestycki-Lions type conditions
PDF Full Text Request
Related items