Research On The Existence Of Positive Solutions For Boundary Value Problem Of P-Laplacian Differential Equations

Nonlinear boundary value problem originates from various of parts of applied math-ematics and physics. It is one of the most active fields that are studied in nonlinear functional analysis. It plays impotant parts in applied mathematics and engineering, es-pecially in the pneumatics and biochemistry aspacts.This paper focus on the existence of positive solutions of boundary value problems with P-Laplacian and fractional boundary value problems,Since the difference of bound-ary conditions in the equations as well as singular points in nonlinear term.the specific methods are used differently in the research.using fixed-point theorem and fixed point in-dex. Sufficient conditions for the existence of positive solutions are given to the boundary value problems.The thesis is organized as follows:The chapter one introduces the historical backgorund of the research questions main-ly. Secondly, it introduces the problems and progress researched in the paper and the main conclusions achieved by the paper.In chapter two,By using Leggett-Williams fixed-point theorem,a class of P-Laplacian Tow-point boundary value problem is studied.Sufficient conditions for the existence of multiple positive solutions are established.In chapter three,By using the lixed point index theorem,a class of Fourth-Order P-Laplacian Operator Singular Boundary Value Problem is considered in weaker condi-tions, two positive solutions are obtained.Moreover, an example is given to illustrate the effectiveness of our results.In chapter four,we consider the three-point.singular boundary value problem for a class of fourth-order P-Laplacian equations by using the fixed point index theory,The conditions of the existence and multiplicity of positive solutions are obtained.In chapter five,using a fixed piont theorem in Banach space, the existence of one positive solution of a class of third-order P-Laplacian coupled boundary value problem is proved in weaker conditions.In chapter six, Constructing a Green function,under mild conditions, we investi-gate the existence and multiplicity of positive solutions for nonlinear fractional differential equation by using Krasnoselkiis fixed-point and Leggett-Williams fixed-point,an im-provement over many known results, Moreover, an example is given to illustrate the effectiveness of our results.