Existence Of Solutions For Two Classes Of Boundary Value Problem Of Impulsive Equations

In this thesis, based on variational methods and critical point theory, we consider the existence of solution of two class of boundary value problems of impulsive differential equations. By choosing suitable spaces and functionals, we get the existence of critical points for the functional with different critical point theorems, so the existence criteria of solution of the corresponding impulse differential equations are established.First, we introduce the background of impulsive differential equation and its recent development. The main results and method of this dissertation are given, and some preliminary knowledge are also listed.Then, we consider the existence of solutions for the following impulsive dif-ferential equation with Sturm-Liouville boundary condition by using mountain pass lemma and symmetric mountain pass theorem, the ex-istence of at least one solution and an infinite number of solutions are obtained. Also, based on a three critical points theorem, under appropriate assumptions, we get the existence of at least three solutions for the problem when the parameterλlies in a explicitly interval. Some examples are also given to illustrate the results.Finally, we study the existence of solutions for the following periodic bound-ary value problem of the impulsive differential equation Where the parameterλis nonnegative, which is different from that in the liter-ature. Using mountain pass theorem and saddle point theorem, we established some existence criteria of at least one solution, sufficient condition of the existence of at least one solution is also given by using a critical point theorem without compact assumption.