Existence Of Solutions To Impulsive Differential Equation For Singular Boundary Problems

This paper mainly discuss the existence of solutions for impulsive singular boundary value problems and initial value problems.Via improve and generalize methods and assumptions in the literature,we use the variational method,critical point theorem mountain pass lemma.t he fixed point theorem to obtain some new results.The full text mainly divides into three chapters.The first chapter deseribes the historical background,research dynamics,main work and preliminary knowledge.The second chapter discuss the existence of solutions to a singuar Dirichlet boundary value problem with impulses,we improve and generalize some existing methods and assumptions in the literature.We take the singular differential e-quation into a nonsingular differential equation at first,then using the variational method to prove the existence of solutions for the nonsingular differential equa-tion.finally solutions of the nonsingular differential equation can be converted into solutions of the singular differential equation,so we obtain the existence of solutions.This chapter is divided into two parts:In the first part,we use the variational method combined with the critical point theorem,proving that the equation has at least one nontrivial solution exists;In the second part,we use the variational method and the mountain pass lemma to prove an infinite number of solutions for impulsive problems.The third chapter discuss the existence of solutions to a singular initial value problem for the impulses,by generalizing some existing assumptions in the litera-ture.We use the method of subsection discussion,taking the singular differential equation into nonsingular differential equations,in this chapter,we use the fixed point theorem to obtain the existence of solutions.