Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON POSITIVENESS AND CONTRACTIVENESS OF THE INTEGRAL OPERATOR ARISING FROM THE BEAM DEFLECTION PROBLEM ON ELASTIC FOUNDATION

  • Received : 2014.08.21
  • Published : 2015.07.31
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Abstract

We provide a complete proof that there are no eigenvalues of the integral operator ${\mathcal{K}}_l$ outside the interval (0, 1/k). ${\mathcal{K}}_l$ arises naturally from the deflection problem of a beam with length 2l resting horizontally on an elastic foundation with spring constant k, while some vertical load is applied to the beam.

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References

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  1. Spectral analysis of the integral operator arising from the beam deflection problem on elastic foundation II: eigenvalues vol.2015, pp.1, 2015, https://doi.org/10.1186/s13661-014-0268-2