Multiple Solutions Of Boundary Value Problems For Impulsive Differential Equations Via Variational Method

In this thesis,the existence and multiplicity of solutions of boundary value problems for three classes of impulsive differential equations are considered by variational method.The main theorems used are Mountain pass theorem,Symmetric mountain pass theorem,Mountain pass theorem under Cerami condition,Symmetric mountain pass theorem under Cerami condition and Fountain theorem under Cerami condition.The thesis contains six parts.The introduction describes the research purpose,background,previous results and our main work.In the first chapter,some basic knowledge including basic definitions,lemmas and theorems are introduced.In the second chapter,the existence and multiplicity of solutions of boundary value problem for the following second-order impulsive differential equations are considered,Under the assumptions that the nonlinearity is super-linear,but doesn't satisfy the Ambrosetti-Rabinowitz condition,and the impulsive functions satisfy the super-linear growth conditions,this problem has at least one solution and infinitely many solutions by using Mountain pass theorem and Symmetric mountain pass theorem.In the third chapter,the existence and multiplicity of solutions of boundary value problem for the following impulsive differential equations with p-Laplacian operator are considered,Under the assumptions that the nonlinearity is super-linear,but doesn't satisfy the Ambrosetti-Rabinowitz condition and the functional satisfies Cerami condition,this problem has at least one solution and infinitely many solutions by using Mountain pass theorem under Cerami condition,Symmetric mountain pass theorem under Cerami condition and Fountain theorem under Cerami condition.In the fourth chapter,the weak solutions of boundary value problem for the following second-order non-instantaneous impulsive differential equations with a perturbation term are considered,Under the assumptions that the nonlinearity is super-quadratic at infinity and subquadratic at the origin,this problem has at least one weak solution by using Mountain pass theorem.In the fifth chapter,the summary of our main work and prospect for the future work are given.