On The Existence Of Positive Solutions For Boundary Value Problems With Delay

Functional differential equations with delays have wide application in problems of physics and variational problems of control theory(see[1]-[3]). Similarly, The boundary value problem with delays are important in many aspects(see[4]-[6]). In recent years, because it can very well explain many phenomena as well as their theoretical system of continuous improvement has been the attention of domestic and international math-ematical community and the natural world. The boundary value problem with delay has become a very important area of modern mathematics.Boundary Value Problems with Time Delay is a hot topic in recent years, there is now extensive research.This paper uses cone theory and fixed point theorem for nonlinear functional methods such as existence of positive solutions for nonlinear with delay of boundary value problems, and obtained some new results.The thesis is divided into three sections according to contents.Chapter1In this chapter, we consider the following third-order boundary value problem with delay whereφp(s)=|s|p-2s,p>1,φp-1=φq,1／p＋1／q=1,α>0, constantl>(?)>0.λ Is a positive real parameter.f∈C([0,1]×[0,∞),[0,∞)),a(t)∈C(0,1)∩L1[0,1],a(t)>0,(?)t∈(0,1). By cone theory of knowledge structure, we have the existence of positive solutions by Guo-Krasnoselskii fixed point theorem.Chapter2In this chapter, discussed below with a delay of singular third-order multi-point boundary value problems where0is contnuous,is continuous.The nonlinear term h(t)f(t,υ)is singular at t=0,t=1and υ=0.The positive solutinS of a class of with delays of singular third-order multi-point boundary value problems are considered by using the Guo-Krasnoselskii fixed point theorem of cone,and given n positive solutions appropriate conditions.Chapter3In this chapter,focuses on the following two categories with a delay of one-dimensional P-Laplacian equations where is a Constants,and is nonnegative continuous at t∈(0,1),and a(t)≠0,t∈(0,1),Using the monotone iterative method to consider the existece of positive solutions for the boundary value problem(3.1.1)(3.1.3) and (3.1.2)(3.1.3)are solutions exist.