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

Abstract EN

We discuss the solvability of the fourth-order boundary value problem u(4)=f(t,u,u′′), 0≤t≤1, u(0)=u(1)=u′′(0)=u′′(1)=0, which models a statically bending elastic beam whose two ends are simply supported, where f:[0,1]×R2→R is continuous.

Under a condition allowing that f(t,u,v) is superlinear in u and v, we obtain an existence and uniqueness result.

Our discussion is based on the Leray-Schauder fixed point theorem.