We discuss the solvability of the fourth-order boundary value problem , , , which models a statically bending elastic beam whose two ends are simply supported, where 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.
Yongxiang Li. He Yang. "An Existence and Uniqueness Result for a Bending Beam Equation without Growth Restriction." Abstr. Appl. Anal. 2010 1 - 9, 2010. https://doi.org/10.1155/2010/694590