Existence Of Positive Solutions For Boundary Value Problems On Time Scales

The concept of dynamic equations on time scales was firstly introduced in 1990 by Hilger. Then it was rapidly becoming the interest of many mathematician. This new theory provides an unified approach to continuous and discrete calculs. The research work on time scales has been extensivly applied in many areas such as the study of insect population models, heat transfer and so on. There are many systemic theories(see our references). This paper discusses some boundary value problems on time scales, and obtains some useful results on the basis of above discussions.There are four chapters in the paper.Chapter 1 investigates the existence of positive solutions for the following boundary value problemwhere h(t) maybe singular at t = 0 and t =σ(1). It is remarkable that when the nonlinear term does not have singularity, such problems on time scales have been studied extensively. Unfortunately, as far as we know, there is no paper concerned with the above problem when the singularity occurs.Chapter 2 investigates the existence of positive solutions for the p-Laplacian boundary value problemwhere h maybe singular at t＝a and t＝b and nonlinearity f maybe negative . Chapter 3 investigates the following m－point boundary value problemwhere (?), and obtains theexistence of at least one positive solution to the above problem.Chapter 4 investigates the existence of at least one solution for the following first-order periodic implusive differential equations...