Existence Of Solutions For The BVP Of A Class Of Ode And Fractional Difference Equation

Nonlinear functional analysis is an important branch of modern mathe-matics. Since it can explain all kinds of natural phenomena, more and more mathematicians are devoting to it.Among them,the nonlinear boundary value problem comes from a lot of branches of applied Mathematics and physics,and it is andysis. One of the most active fields that is studied in the mathematics.The present paper employs the cone theory,fixed point theory,and topological degree theory and so on,to investigate the existence of solutions of several classes of differential equations singular boundary value problem.The obtained results are either new or intrinsieally generalize and improve the previous relevant ones under weaker conditions.According to contents,the paper is divided into several sections as follows.The introduction is mainly about backgroud of this paper.In the first chapter,we are devoted to establish the multiplicity of positive solutions to positone superlinear singular equations with periodic boundary con-ditions,by using the fixed point theorem of cone expansion and cone compression and Leray-Schauder nonlinear alternative theorem.In the second chapter,by using the Leray-Schauder nonlinear alternative the-orem, we research the existence of solutions for a class of Caputo type fractional differential equations boundary value problems.In the third chapter,by using Leggett-Williams fixed point theorem,the fixed point theorem of cone expansion and cone compression and the property of Green fuction,we research single and multiple solutions for a class of Riemann-Liouvile fractional differential equation boundary value problems.