Existence Of Solutions For Several Classes Of Kirchhoff Type Elliptic Systems

This article aims to discuss the properties of the solutions of two kinds of Kirchhoff type partial differential systems on unbounded regions using variational methods such as the Mountain Pass Theorem,Ekeland's variational principle,Nehari manifold and fibering map.The full text is divided into four chapters:In Chapter 1,we explains the relevant background and current situation of the equations discussed in this article,and gives the required theoretical knowledge.In Chapter 2,we consider the following inhomogeneous p-Kirchhoff type partial differential equations on unbounded domains(?)where ?,?>0,1<p,N,1<q<p<p(k+1)<?+?<p*=Np/N pd,0?a<N-p/p,a?b<a+1,d=a+1-b>0,M(s)=a+bsk,k?0.H(x),h1(x),h2(x),l1(x)and l2(x)are continuous functions and can change signs on RN.This chapter uses the Mountain Pass Theorem and Ekeland's variational principle to give two non-negative solutions to the pr-oblems discussed above.In Chapter 3,we explore the following Kirchhoff type partial differential systems#12 where ?,?>0,1<p<N,1<m<p<p(?+1)<d ?<p*=Np/N-p,0?a<N-p/p,a?b<a+1,M(s)=k+ls?,k>0,l?0,?>0.This chapter uses the Nehari manifold and the fibering map methods to solve that when the parameter(?,?)belongs to a certain subset of R2,this system of equations has two positive solutions.In Chapter 4,summarizes the full text and looks forward to the future research.