An Existence and Uniqueness Result for a Bending Beam Equation without Growth Restriction

We discuss the solvability of the fourth-order boundary value problem (4)=(,,), 0≤≤1, (0)=(1)=(0)=(1)=0, which models a statically bending elastic beam whose two ends are simply supported, where ∶[0,1]×？2→？ is continuous. Under a condition allowing that (,,) is superlinear in and , we obtain an existence and uniqueness result. Our discussion is based on the Leray-Schauder fixed point theorem.