Linear With P-Laplace Operator With A Class Of Boundary Value Problems For Traveling Wave Solutions Of Reaction-diffusion Equation Problem

In the theory of the linear ordinary differential equation,the solutions of thenonlinear boundary value problems and the traveling wave solution of thereaction-diffusion equations are the main problems.This paper discusses thenonlinear boundary value problems with p-Laplace operator and the traveling wavesof the reaction-diffusion equations.In chapter1, this paper introduce the development survey and main researchdirections of the linear boundary value problem,the p-Laplace operator and thetraveling waves problems,Summarizes the main content and Implications for researchof this paper.In chapter2, we discuss some basic theory that relate to this paper.In chapter3, we first introduce some concept of the linear boundary valueproblems,and resolve the exist of the solution to the nonlinear boundary valueproblems.We first give the expression of the linear boundary value problems withp-Laplace operator.Then by monotone iterative method,sufficient condition forextreme solution are obtained.In chapter4,we first introduce some concept of the traveling wave solutions andthe usual processing method,and the uniqueness of monotone mono-stable wavesfor reaction-diffusion equations.We first give the expression of the reaction-diffusion equations,then prove theexistence the monotone mono-stable of traveling wave fronts.