Existence Of Solutions For Fourth-order Impulsive Differential Equations

In this paper, we mainly study two kinds of fourth-order solutions for the existence and multi solution of impulsive differential equations boundary value problems, We set up different variational constructer in Banach space, and use division method and critical point theory equation to study existence and multiple solutions for equations in different boundary conditions. This paper is divided into three chapters.In chapter one. This article introduces the historical background of the dif-ferential equation and the main research methods of pulse, and briefly introduces the main content of this paper.In chapter two,We research on Sturm - Liouville value conditions for a class of fourth-order nonlinear impulsive differential equations, This article by using the minimum principle, mountain pass lemma and the three critical points theorem to prove the existence and multiple solutions of the equation.In chapter three, By using the critical point theorem and mountain pass lem-ma,This article study the existence of solutions for four order nonlinear impulsive differential equations with Drichlet boundary conditions.