Existence and uniqueness of solutions for a fourth-order boundary value problem

In this paper, we study the fourth-order two-point boundary value problem x⁗(t)−f(t,x(t),x′(t),x″(t),x‴(t))=0,t∈(0,1),x(0)=x′(1)=0,ax″(0)−bx‴(0)=0,cx″(1)+dx‴(1)=0. By means of lower and upper solution method, growth conditions on the nonlinear term ff which guarantee the existence of solutions for the above boundary value problem are given. In particular, we obtain the uniqueness of the solution by imposing a monotone condition of the term ff.