Positive Solutions Of Boundary Value Problems For Differential Equations With P-Laplacian Operators

Nearly,the theory of the fractional differential equation is always a valuable applied instrument of a variety of fields.In particular mathematica affairs,the theory of the fractional differential equation is playing increasingly important role in that.So more and more professors all over the world keep a watch eye on researching the fractional differential equation,and the boundary value problems of nonlinear fractional differential equations with p-Laplacian operator are also paid attention.In this paper,we study the boundary value problems of nonlinear fractional differential equations with p-Laplacian operator,it is divided into four chapters.The first chapter introduces the history and evolution,and the relevant definitions of p-Laplacian operator together with some basic properties and lemmas are given.The second chapter researches the multiple boundary value problems with pLaplacian operator(?)In this note,according to the properties of the Green function,the existence of the solution is obtained by using the Schauder fixed point theorem,and the existence of the maximal and minimal solutions are obtained by using the monotone iterative method.The third chapter researches the m-point boundary value problems of fractional differential equation on infinite intervals This note obtains the existence and multiple of the solutions to the fractional differential equation,by means of the fixed point theorem.The forth chapter study solutions of the multi-point boundary value problem of nonlinear fractional differential equation involving the p-Laplacian operator on infinite intervals(?)This note studies the existence and multiple of solutions,by means of the fixed point theorem of cone expansion and compression and combining with the properties of the Green function.