Existence And Multiplicity Solutions Of Second-Order Impulsive Differential Equations

This paper mainly study the existence and multiplicity of two second-order impulsive differential equations. With different impulsive equations, different vari-ational structure are set up to establish the existence and multiplicity results via the classical variational techniques and critical point theory. This paper consists of three chapters.In Chapter 1, this article outline the critical point theory, preparations, his-torical background and the main works of this paper.In Chapter 2, this article study the existence and multiplicity of some kinds of second-order impulsive differential equations. Firstly, this article establish the corresponding functional equations, boundary value problems for the equation into the critical point of functional problems, Then, in the conditions that without verification (p.s.), by using the three critical points theorem, this article proves the existence and multiplicity of solutions of equations.In Chapter 3, this article uses the the variational method, minimization prin-ciple, mountain pass lemma to study another second-order impulsive differential equations existence and multiplicity of solutions.