Third-order Boundary Value Problems With Integral Boundary Conditions

Boundary value problems with integral boundary conditions not only include two point and multi-point boundary value problems, but also can more accurately describe a lot of important phenomenons. For example, in the field of heat conduc-tion, chemical engineering, underground water flow, thermo-elasticity and plasma physics, a lot of problems can be reduced to boundary value problems with integral boundary conditions. This promote us to study the existence and multiplicity of positive solutions for such problems.In chapter two, by using Leggett-Williams fixed point theorem, we study the third-order boundary value problem with integral boundary conditions where f∈C([0,1] x [0,+∞),[0,+∞)) and g∈C([0,1],[0,+∞)). The existence of at least three positive solutions for the above boundary value problem is obtained.In chapter three, the existence of at least one or two monotone positive solu-tions and nonexistence are studied for the third-order boundary value problem with integral boundary conditions where f∈C([0,1] x [0,+∞) x [0,+∞),[0,+∞)) and g∈C([0,1],[0,+∞)). The main tool used is the Guo-Krasnoselskii fixed point theorem.In chapter four, by means of iterative technique, we continue to study the boundary value problem in chapter three. The existence of monotone positive so-lutions is obtained. Moreover, the iterative schemes start off with zero function or linear function, which is useful and feasible for computational purpose.