Existence Of Positive Solutions For Multi-point Boundary Value Problems

In recent years there has been an increasing interest in multi-point boundary problems. This thesis studies mainly the existence and multiplicity solutions for these problems. The main results are summarized as follows:Firstly, we consider the existence of countable many positive solutions for nonlinear singular boundary value problems by using a fixed point theorem for operator on a cone.Secondly, we study the existence of countably many positive solutions of boundary value problems on the half-line for differential equations of second order. The fixed-point index theory and a new fixed point theorem in cones are used.Thirdly, we use the fixed point theorems and the lower and upper solution method, some results on the existence of positive solutions to the 2(n - m)-point boundary value problems are obtained. At the same time, the results obtained generalize and improve the corresponding results of Chen [8].