Positive Solutions For Several Classes Of Three-Point Boundary Value Problems Of Nonlinear Third-Order Differential Equations

Third-order differential equations arise in a lot of different areas of applied mathematics and physics, e.g., in the defection of a curved beam having a constant or varying cross, section, a three-layer beam, electromagnetic waves or gravity driven flows and so on. Recently, three-point boundary value problems (BVPs for short) for third-order differential equations have received much attention. Therefore, it is significant to study positive solutions of three-point BVPs of third-order differential equations.In this thesis, we first investigate positive solution for a class of nonlinear third-order three-point BVP by using monotone iteration method. The existence of positive solutions is obtained and two iterative sequences of positive solutions are given. Second, we are concerned with a class of nonlinear third-order three-point BVP, where nonlinear term contains first derivative of unknown function. By applying iterative techniques, we not only obtain the existence of monotone positive solutions, but also two iterative sequences of monotone positive solutions are given. It is worth mentioning that these iterative schemes start off with zero or linear functions, which is very useful and feasible for computational purpose. Finaly, we consider a class of nonlinear singular third-order three-point BVP with a parameter by using Guo-Krasnoselskii fixed point theorem. Under suitable conditions, we investigate the effect of parameter on the existence of positive solutions.