Solvability Of A Class Of Fully Fourth-order Ordinary Differential Boundary Value Problem

In this paper,by using fixed point theorem of completely continuous operators,the method of upper and lower solutions and the fixed point index theory in cones,we discuss the existence and uniqueness of solutions and the existence of positive solutions to fully fourth-order boundary value problem for ordinary differential equations with two simple supports(?) where f:[0,1]×R4?R is a continuous function.The main results of this paper are as follows:1.By choosing a convex closed set,we obtain the existence and uniqueness of solutions to fully fourth-order ordinary differential boundary value problem by using the Schauder fixed point theorem of completely continuous operators under conditions that the nonlinear term contains primary growth condtion.2.The existence and uniqueness of solutions to complete fourth-order boundary value problems are obtained by using the Leray-Schauder fixed point theorem of all continuous operators under the condition of allowing nonlinear term to satisfy one-side superlinear growth conditions and Nagumo type growth conditions.3.The existence of a solution of a completely fourth-order boundary value problem was obtained by using a special truncation technique using the upper and lower solution method in the case of introducing Nagumo-type growth conditions.4.By establishing a new maximum principle of fourth-order boundary value problem,we obtain the existence of positive solutions to fully fourth-order ordinary differential boundary value problem is obtained on the basis of section 3.