With P-laplacian Operator Subtypes Of Singular Boundary Value Problems Existence Of Positive Solutions

Recently,a major breakthrough has achieved in nonlinear functional analysisdevelopment. It is an important branch of mathematics, and it can explain several kinds of natural phenomena. The singular boundary value problems for nonlinear differential equations has a extensive background of mathematics and physics,so it is at present one of the most active fields in analyse mathematics.Among them,the existence of positive solutions for nonlinear singular boundary value problems with p-Laplacian comes from, a lot of branches of applied mathematics and physics, and it is very meaningful in both practical and theoretica aspects,so many Chinese and foreign scholars are paying attentionit. The present paper employs the cone theory, fixed point theory and a new fixed point theorem in cone and so on, to investigate the existence of positive solutions to some kinds of nonlinear singular boundary value problems with p-Laplacian.The results obtained are either new or essentially generalize and improve the previous relevant ones under weaker conditions.The thesis is divided into three chapters according to contents.In chapter l,we discuss the existence of positive solutions for a class of singular boundary value problems with p-Laplacianwhereφ_p(s)=|s|^p-2s,p>1,(φ_p)^-1=φ_q,1/p+1/q=1,α>0,β≥0,γ>0,δ≥0,the singularity may appear at t = 0,1. By using the cone theory and a new fixed point theorem in cone,the existence of positive solutions for this singular boundary value problems with p-Laplacian are obtained. Under the conditions of f is dependent on derivative of one order,we show that there exist a continuous and convex function (?)(u) and the positive numbers L, b, c such that the boundary value problems (1.1.1) has at least a positive solution u(t), u(t) satisfying c < (?)(u) < b,|u'(t)| < L .The theorem improves and generalizes the boundary value problems of [16] essentially and the result is significantly different from [16].In Chapter 2, we discuss the existence of infinitely many positive solutions for a class nonlinear singular boundary value problems with p-Laplacianwhereφ_p(s)=|s|^p-2s,p>1,(φ_p)^-1=φ_q,1/p+1/q=1,α>0,β≥0,γ>0,δ≥0 .By using the cone theory and a new fixed point theorem in cone yet, theexistence of positive solutions for this singular boundary value problems with p-Laplacian are obtained.Under the conditions of f is dependent on derivative of one order, we show that the boundary value problems (2.1.1) has infinitely many positive solutions.The theorem popularizes the f of [3] such that f is dependent on derivative of one order,so the method is significantly different from [3].The chapter improves and popularizes the chapter 2.In Chapter 3,we discuss the existence of positive solutions for a class of nonlinear singular boundary value problems with p-Laplacianwhereφ_p(s)=|s|^p-2s,p>1,(φ_p)^-1=φ_q,1/p+1/q=1,the singularity may appearat t = 0,1. By using a new fixed point theorem in cone,the sufficient conditionsfor this nonlinear singular boundary value problems with p-Laplacian is obtained. Under the conditions of f is dependent on derivative of one order, we discuss the boundary value problems (3.1.1),so the chapter popularizes and improves [4].