Existence of solutions for a fully nonlinear fourth-order two-point boundary value problem

In this paper, we investigate the existence of solutions of a fully nonlinear fourth-order differential equation x(4)=f(t,x,x′, x″,x″′, [t∈[0,1 with one of the following sets of boundary value conditions; x′(0)=x(1)=a0x″(0)-b 0x″′(0)=a1x″(1)+b 1x″′(1)=0, x(0)=x″(1)=a0x″(0)- b0x″′(0)=a1x″(1)+b 1x″′(1)=0 By using the Leray-Schauder degree theory, the existence of solutions for the above boundary value problems are obtained. Meanwhile, as an application of our results, an example is given. © 2010 Korean Society for Computational and Applied Mathematics.