Applications Of Critical Point Theory To Boundary Value Problems For Second-order Impulsive Differential Equations(Systems)

In this thesis,we mainly study the existence and multiplicity of solutions for three second-order impulsive differential equations(systems).By using variational methods and critical point theory,different variational structures are constructed and obtain the existence of at least one or multiple solutions for these equations.Our results are mainly consist of five chapters as follows:The introduction describes the historical background,current situation and trend of the research about impulsive differential equations(systems)briefly.Then,some basic knowledge of nonlinear functional analysis,variational methods and critical point theory are listed.Moreover,the advantages of variational methods for studying impulsive differential equations(systems)is pointed out.At last,the main work of this thesis is introduced.In Chapter 1,multiple solutions for a class of non-linear second-order impulsive differential equations with parameter dependence are studied.By using variational methods and critical point theory,the existence of at least one and three weak solutions are obtained,which extends the results in the related literatures.In Chapter 2,the existence and multiplicity of solutions for a class of secondorder differential equations with non-instantaneous impulses are studied.By using mountain-pass theorem,several important theorems are obtained to ensure the existence of at least two weak solutions and infinitely many weak solutions for the problem.Our results are new.In Chapter 3,a class of second-order impulsive differential systems boundary value problem is considered.By critical point theory,the existence of unique solution,at least one solution and infinitely many solutions are proved.Our results extend the previous research for the problem.In Chapter 4,we summarize this thesis and discuss the future research directions.