An Existence and Uniqueness Result for a Bending Beam Equation without Growth Restriction
Keyword(s):
We discuss the solvability of the fourth-order boundary value problemu(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, wheref:[0,1]×R2→Ris continuous. Under a condition allowing thatf(t,u,v)is superlinear inuandv, we obtain an existence and uniqueness result. Our discussion is based on the Leray-Schauder fixed point theorem.
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