The Existence Of Symmetric Solutions For Two Types Of Boundary Value Problems With Integral Boundaries

With the development of society,boundary value problems has been getting more and more attention on its widely uses in physics,biological,chemistry.etc.In recently years,both depth and breadth aspect of the boundary value problem has been making great,progress.Readers can see Refs.[1-18].for details.The research methods of solving the problems in this fields arp been getting more and more improvement.Such as,fixed point theorems,upper and lower solutions coupled with monotone iterative method,coincidence degree theory,etc.In 2015,Abdlkadir Dogan studied the symmetric solutions of second order differential equations by the Leggett-Willians fixed point theorem.Two kinds of boundary value problems are studied the existence of symmetric solutions by using Leggett-Williams fixed point theorem in this paper.In Chapter one,we introduce the meaning and the background of our research,and the problem to be solved in this paper.In Chapter two,we investigate a class of third-order impulsive differential equations with integral boundary values.By a generalized Leggett-Williams fixed point theorem,we prove the system has at least three symmetric position solutions.Meanwhile,an example to demonstrate the main result is given.In Chapter three,we consider the existence of solutions for a class of fourth-order impulsive differential equations with integral boundary value conditions.First of allwe divided the problems into two second-order systems,Second,We studied the nature of the green's function,Lastly,Second By imposing growth conditions on f and using a generalized Leggett-Williams fixed point theorem,we prove the system has at least three symmetric positive solutions.