Existence And Multiplicity Of Solutions For Boundary Value Problems On Infinite Intervals

This paper is concerned with the existence and multiplicity of solutions for boundary value problems on infinite intervals by using the Guo-Krasnosel'skii fixed point theorem, upper and lower solutions method, topological degree theory and fixed point index theory.In Chapter 1, we shortly introduce related background and recently develop-ment about boundary value problems on the half line and the main contents of the thesis.In Chapter 2, we mainly study the following boundary value problem on infinite intervals where k is a positive constant and f ? C([0, ?) x [0,?,[0,?)). In a suitable space, the existence of at least one positive solution is obtained using the Guo-Krasnosel'skii fixed point theorem. Furthermore, the following boundary value problem with the nonlinear term involved in the first-order derivative will also be considered Under some suitable conditions, we establish the existence of positive solution result by making use of the Guo-Krasnosel'skii fixed point theorem combining with the properties of Green function.In Chapter 3 , we focus on the existence of multiple solutions for boundary value problem on infinite intervals which nonlinear term does not contain the first-order derivative in Chapter 2. Under given conditions, we establish the existence of at least three solutions by making use of the upper and lower solutions method and the topological degree theory.In Chapter 4, we discuss the following boundary value problem with respect to parameter where A is a positive parameter and h,g ? C([0, ?), (0, ?)). Under some suitable assumptions, employing upper and lower solutions method and fixed point index theory, a global result for boundary value problem on infinite intervals with respect to parameter is obtained, namely, the existence, nonexistence and multiplicity of positive solutions.