We study the existence and multiplicity of solutions of the fourth order nonlinear boundary value problem , , is assumed to be positive, continuous and increasing in .
We prove that there exists a such that there is always a solution for can be . From our results it follows that if is bounded (for in some compact interval around then there exists such that there is no solution for .
We provide conditions on such that there are at least two solutions for . Degree theory is used to prove this result.