Existence and Uniqueness of Nonlinear Three-Point Boundary Value Problem for Third Order Equation

In this paper, nonlinear three-point boundary value problems for a class of third order nonlinear differential equations is studied by means of differential inequality theories and upper and lower solutions. Based on the given results of second order boundary value problem, and under suit upper and lower solution, iteration sequences were constructed, and existence and unique of solutions of nonlinear boundary value problems of second order nonlinear Volterra type integro-differential equation were obtained by means of applying the Arzela-Ascoli theorem and Lebesque control convergence theorem and disproof method. Finally, the existence and uniqueness of solution for three-point nonlinear boundary value problems were established. The result showed that is seems new to apply these technique to solving other boundary value problems.