Multi-point Boundary Value Differential Equations, With P-laplacian Operator

The BVPs with p-laplacian arise in a variety of applied areas such as applied mechanics,astrophysics and nonlinear partial di?erential equations. The paper studies the boundaryvalue problems for ordinary di?erential equation with p-laplacian operator by using ?xedpoint theorems. Firstly, we get the su?cient condition of the existence of at least three posi-tive solutions for the BVPs with p-laplacian of nonlinear term with the ?rst order derivativeof unknown function on in?nite intervals. In addition, we study multi-point boundary valueproblem with p-Laplacian of nonlinear term with the ?rst order derivative of unknown func-tion on (0,1)The paper consists of four chapters:In chapter 1, we mainly introduce the background and the progress of the multi-pointBVPs with p-laplacian. In addition, we also present the organized of this paper.In chapter 2, we get at least three positive solutions ofby using the Avery-Peterson's ?xed point theorem.In chapter 3, we get at least three positive solution ofby using Bai and Ge ?xed point theorem.In chapter 4, we get the su?cient condition of the existence of at least three positivesolutions for withby using the Avery-Peterson's ?xed point theorem.