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Some multiplicity results for an elastic beam equation at resonance

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Abstract

This paper deals with multiplicity results for nonlinear elastic equations of the type

$$\begin{gathered} - d^4 u/dx^4 + \pi ^4 u + g(x,u) = e(x) (0< x< 1) \hfill \\ u(0) = u(1) = u''(0) = u''(1) = 0 \hfill \\ \end{gathered}$$

where g:[0, 1]×R→R satisfies Caratheodory condition e∈L2[0,1]. The solvability of this problem has been studied by several authors, but there isn't any multiplicity result unitl now to the author's knowledge. By combining the Lyapunov-Schmidt procedure with the technique of connected set, we establish several multiplicity results under suitable condition.

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Authors and Affiliations

  1. Department of Mathematics, Northwestern Teachers University, Lanzhou

    Ma Ru-yun

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  1. Ma Ru-yun
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Communicated by Chien Wei-zang

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Ru-yun, M. Some multiplicity results for an elastic beam equation at resonance. Appl Math Mech 14, 193–200 (1993). https://doi.org/10.1007/BF02453362

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  • DOI: https://doi.org/10.1007/BF02453362

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