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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.

Suggested Citation

  • Yongxiang Li & He Yang, 2010. "An Existence and Uniqueness Result for a Bending Beam Equation without Growth Restriction," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    • Handle: RePEc:wly:jnlaaa:v:2010:y:2010:i:1:n:694590
    DOI: 10.1155/2010/694590
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    References listed on IDEAS

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    1. Klaus Deimling, 1985. "Nonlinear Functional Analysis," Springer Books, Springer, number 978-3-662-00547-7, October.
    2. C. De Coster & C. Fabry & F. Munyamarere, 1994. "Nonresonance conditions for fourth order nonlinear boundary value problems," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 17, pages 1-16, January.
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    Cited by:

    1. Y. Y. Lee & A. Y. T. Leung & B. Zhu, 2012. "Structural‐Electrical‐Coupled Formulation for the Free Vibration of a Piezoelectric‐Laminated Plate Using the Analytical Arbitrary Quadrilateral p Element," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. Serry, Mohamed A. & Peterson, Sean D. & Liu, Jun, 2025. "Static Euler–Bernoulli beams with contact forces: Existence, uniqueness, and numerical solutions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 238(C), pages 269-279.

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