Sign-changing Solutions For Two Classes Of Quasilinear Nonlocal Problems

This master's thesis consists of four chapters:In chapter 1,we firstly introduce the background and the current research situation of two kinds of generalized Schrodinger-Poisson system and Kirchhoff-type equation.Then briefly introduced the main results of this paper.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 so-lution for generalized quasilinear Schrodinger-Poisson system.Under suitable con-ditions on f,g,by using constraint variational method and the quantitative defor-mation lemma,if ? is large enough,we obtain a ground state sign-changing solution to this problem for each ?>0 and its energy is strictly larger than twice that of the ground state solutions.In chapter 4 we study the existence of the ground state sign-changing solu-tion for generalized quasilinear Kirchhoff-type equation,Under suitable conditions on f,g,by using constraint variational method and the quantitative deformation lemma,if ? is large enough,we obtain a ground state sign-changing solution to this problem for each b>0,and its energy is strictly larger than twice that of the ground state solutions.