Nodal solutions for a nonlinear fourth-order eigenvalue problem

We are concerned with determining the values of ., for which there exist nodal solutions of the fourth-order boundary value problem y....=.a(x)f(y),0<x<1,y(0)=y(1)=y..(0)=y..=(1)=0, where . is a positive parameter, a . C([0, 1], (0, .)), f . C (., .) satisfies f(u)u > 0 for all u . 0. We give conditions on the ratio f(s)/s, at infinity and zero, that guarantee the existence of nodal solutions. The proof of our main results is based upon bifurcation techniques