Study On Sign-changing Solutions For Two Classes Of Kirchhoff-type Problems

This master’s thesis consists of four chapters:In chapter 1,the background of two kinds of Kirchoff-type systems studied in this paper and the present research situation at home and abroad are briefly introduced.In chapter 2,we give a brief introduction to some of the notations,definitions and relative knowledge used in this paper.In chapter 3,we investigate the existence of the ground state sign-changing solution for the following p-Laplacian Kirchhoff-type equation,and study the energy property of u0.(?)whereΩ(?)RN is a smooth bounded domain,a,b>0,4≤2p<g<p*and N>p.In chapter 4 we study the existence of the ground state sign-changing solution for the following Kirchhoff-type equation,and study the energy property of ub.Moreover,we investigate the asymptotic behavior of Ub as the parameter b↘0.where V,K∈C(R3,R+),f:R→R.There exists a θ0∈(0,1)such that:(?).