Existence And Multiplicity Of Solutions For Several Kirchhoff Type Equations With Zero Mass

In this paper,existence and multiplicity of nontrivial solutions for several Kirchhofftype equations with zero mass are studied via Variational methods and critical point theory.The main content of this article is as follows.Chapter 1 mainly introduces the research background and significance of the Kirchhofftype equation,as well as the research present situation.In chapter 2,we give some basic function spaces and properties,and some abstract critical point theorems.In chapter 3,the existence of ground state solutions for a class of quasi-critical Kirchhofftype equations with zero mass is studied.Under some appropriate conditions,two existence results for ground state solutions of it are obtained by using Variational methods.In chapter 4,the existence of ground state solutions for a class of Kirchhoff type equations with critical terms and zero mass is studied.Under some appropriate conditions,the existence for nontrivial solutions of Kirchhoff type equations with critical terms is proved by using the Variational methods and the Mountain Pass theorem.The second Concentration Compactness lemma is used to prove that the functional associated to the equation satisfies Palais-Smale condition when the energy level is below a certain value.In chapter 5,we study the multiplicity of solutions for a class of critical Kirchhoff-type equations involving p-Laplace operator with zero mass.The lack of compactness in critical problem is overcome mainly based on the second Concentrated Compactness lemma.The multiplicity of nontrivial solutions of the original problem is obtained by using a variant form of Clark's theorem.