We investigate the existence of solutions and positive solutions for a nonlinear fourth-order differential equation with integral boundary conditions of the formx(4)(t)=f(t,x(t),x′(t),x′′(t),x′′′(t)),t∈[0,1],x(0)=x′(1)=0,x′′(0)=∫01h(s,x(s),x′(s),x′′(s))ds,x′′′(1)=0, wheref∈C([0,1]×ℝ4),h∈C([0,1]×ℝ3). By using a fixed point theorem due to D. O'Regan, the existence of solutions and positive solutions for the previous boundary value problems is obtained. Meanwhile, as applications, some examples are given to illustrate our results.
Existence of Positive Solutions of Fourth-Order Problems with Integral Boundary Conditions
