Existence Of Symmetric Solutions For Two Types Of BVP With Integral Boundary Conditions

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 research methods of our research,theorem and the main conclusions of this article,and the problem to be solved in this paper.In Chapter two,the existence of symmetric solutions for second order differential equation boundary value problems with integral boundary are studied.First of all,work out green function and studied the nature of the green's function with integration method;Secondly,the solution of the original system can be divided into two parts in the case of some assumptions,The application of the Leggett-Williams fixed point theorem to the main conclusion through the establishment of composite operator again lastly.In Chapter three,the existence of symmetric solutions of the fractional differential equation boundary value problem with integral boundary are studied.The expression of CD? fractional derivative and nature of Green's function are obtained,the existence of symmetric solutions by using Leggett-Williams fixed point theorem.The difference from others,this article explores the integral boundary and establishing composite operator symmetric to get the existence of positive solutions.Lastly,the correctness of the conclusions are verified by the corresponding examples.