The Existence Of Multiple Solutions For Two Boundary Value Problems Of Impulsive Differential Equations

The thesis consists of four chapters. We study the existence and multiplicity for some damped Dirichlet nonlinear impulsive equations and fourth-order impulsive differential equations by using the variational methods.The chapterl is preface, we present the background and history on boundary value problems and variational methods for nonlinear impulsive differential equations and clarify the significance of the research.In chapter2, we consider the existence and multiplicity of solutions for some damped Dirichlet nonlinear impulsive differential equations by using the variational methods. On the basis of related references, we will establish some new existence criteria to guarantee that the problem has one or infinitely many solutions under the assumptions that a nonlinear term satisfies sublinear, superlinear, asymptotically linear. We extend and improve some recent results. What’s more, we give two examples to illustrate our main results.In chapter3, we study the existence and multiplicity of solutions for fourth-order impulsive differential equations. By using the variational methods and critical point theory, we gives some new criteria to guarantee that the impulsive problem has at least one nontrivial solutions, respectively,two examples are given in this paper to illustrate the feasibilities of our results.In chapter4, we make a briefly review about the main works of this paper.