The Positive Solutions For Kirchhoff-Schrodinger-Poisson System With Singularity

At present,nonlinear partial differential equations have become the main body of the research of differential equations.Many significant natural sciences and engi-neering problems can be classified as nonlinear partial differential equations.Many mathematical models in real life can be described by nonlinear partial differential equations.Many important basic equations of physics,mechanics and other sci-ences themselves are described by nonlinear partial differential equations.As the research progress,some problems which used to approximately treated by linear differential equations must also consider the influence of nonlinearity.Therefore,the research of nonlinear partial differential equations,especially the exact solution of nonlinear partial differential equations solution,has shown many important theoretical and applied values.The paper mainly uses Nehari manifold and Ekeland's variational principle to obtain the result of the existence of the positive solutions of the Kirchhoff-Schrodinger-Possion system with singularity.It mainly includes the following three chapters.In chapter 1,we mainly introduce the research status of Kirchhoff-Schrodinger-Poisson system and stipulates some basic knowledge and symbols commonly used in this paper.In chapter 2,the following Kirchhoff-Schrodinger-Poisson system is discussed where a>0,6>0,e = ±1,?>0.We can get the only positive solution of the problem by using the variational method when e = 1.We uses the Nehari manifold to get one positive at least.The two solution of this problem are obtained by using the Ekeland variational principle.In chapter 3,we consider the following Kirchhoff-Schrodinger-Poisson system.Whenthe only positive solution of the problem is obtained by the variational method.When e =-1,we use the Ekeland variational principle,this problem can be obtained respectively by at least one positive solution.