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

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  • Yongxiang Li
  • He Yang

Abstract

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.

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Handle: RePEc:wly:jnlaaa:v:2010:y:2010:i:1:n:694590
DOI: 10.1155/2010/694590
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