Nonlinear Differential Equations For Second Order Multiple-point Boundary Value Problems

In this paper, by using the cone theory, the operator theory, topological approach and the critical point theory ,we study the existence and multiplicity of solutions for several classes of nonlinear differential equations for second order boundary value problems, Some new results are obtained, some relevant results are extended and improved. The structure of this paper as follows.In the first chapter, we introduce the background of the discussed problem of this thesis briefly, and we state the main results of this thesis concretely.In the second chapter, we investigate the multiplicity of solutions for the second-order nonlinear differential equation three-point boundary value problem Whereη∈(0,1),α∈(0 ,1), I =[0 ,1], By using the cone theory and Amann three-solution theorem, we obtain that above BVP has at least three nonnegative solutions under some conditions with its corresponding Green's funtion.In the third chapter, we study the second-order nonlinear impulsive differential equation three-point boundary value problem By using the improved Leggett-Williams'three-solution theorem, we are able to guarantee that the above BVP has at least three solutions.In the fourth chapter, we investigate the second-order nonlinear impulsive differential equation three-point boundary value problem By using topological approach , we obtain that there are at least three solutions under the two lower and upper solutions conditions.In the fifth chapter, we study the second-order nonlinear differential equation two-point boundary value problem By using the critical point theory, We prove the existence of infinite solutionstheorem.