Nodal solutions of boundary value problems of fourth-order ordinary differential equations

We study the existence of nodal solutions of the fourth-order two-point boundary value problemy⁗+β(t)y″=a(t)f(y),00f(u)u>0 for all u≠0u≠0. We give conditions on the ratio f(s)/sf(s)/s at infinity and zero that guarantee the existence of nodal solutions. The proof of our main results is based upon bifurcation techniques.