Existence Theorey For Single And Multiple Positive Solution To Singular Boundary Value Problems For Second-order Differential Systems With P-Laplacian

Along with science’s and technology’s development,various nonlinear prob-lem has aroused people’s widespread interest day by day,and so the nonlinear analysis has become one important research directions in modern mathematic-s. The nonlinear functional analysis is an important branch in nonlinear analy-sis,because it can explain well various the natural phenomenon.In this paper we present some new existence results for singular boundary value problems where φ(s)=|s|p-2,s. p>1, qi(t)(i=1,2) may be singular at t=0or t=1, nonlinearity fi(t,x,y)(i=1,2) may be singular at (x,y)=(0,0). The existence result is obtained via fixed point theorem in cones and Leray-Sehauder alterna-tive.The present work is a direct extension of some results in [26,27,28] for the singular problem, namely, fi(t,x,y) is singular at (x,y)=(0,0).Our technique relies essentially on Leray-Schauder alternative theorem and fixed point theorem in cones in [26,27,28],which we believe is well adapted to this type of problem. We extented the results of p=2to p≠2using Leray-Schauder alternative theorem and fixed point theorem in cones in [26.27,28]. This thesis is composed of three parts. In the first part, we introduces the historical background of problems which will be investigated and the main promlem studied in this paper,namely the singular boundary value problems of the second-order differential systems p-Laplace. There is a brief summary of results of this problem in other literatures, and introduction of some basic knowledge and propositions which will be needed in the proof of the theorem.In the second part, we establish existence principles for nonsingular Dirichlet boundary value problem to the second-order p-Laplacian. In this part, we will using contents and methods from [26,27,28].The last part is about the main findings of the present study, we establish and prove the existence theorem for single and multiple positive solutions to singular and nonsingular Dirichlet boundary value problems for the second-order differential systems p-Laplacian. The proof of these theoriems adopt the results of the part two.