Solvability Of A Class Of Fully Third-Order Ordinary Differential Boundary Value Problem

In this paper,by using fixed point theorem of completely continuous operators,the fixed point index theory in cones and the method of upper and lower solution-s,we discuss the existence and uniqueness of solutions and the existence of positive solutions to fully third-order ordinary differential boundary value problem where f:[0,1]× R3? R is a continuous function.The main results of this paper are as follows:1.With the aid of the existence and uniqueness of solutions for corresponding third-order linear differential equation,we obtain the existence and uniqueness of solutions to fully third-order ordinary differential boundary value problem by using the Leary-schauder fixed point the orem of completely continuous operators under the linear growth conditions.2.Under the superlinear growth conditions and Nagumo-type growth condi-tion.we obtain the existence of solutions to fully third-order ordinary differential boundary value problem by using the Leary-schauder fixed point theorem of com-pletely continuous operators.3.By choosing a special cone and applying the fixed point index theory in cones,we obtain the existence of positive solutions to fully third-order ordinary differential boundary value problem under the case of superlinear and sublinear conditoins.4.Under the Nagumo-type growth condition,we obtain the existence of solu-tion and postive solutions to fully third-order ordinary defferential boundary value problem via the lower and upper solution method and a special truncating technique.