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ON POSITIVENESS AND CONTRACTIVENESS OF THE INTEGRAL OPERATOR ARISING FROM THE BEAM DEFLECTION PROBLEM ON ELASTIC FOUNDATION

최성우
대한수학회 (The Korean Mathematical Society)|2015.07|대한수학회보 (Bulletin of the KMS)|제52권 제4호|pp. 1225-1240

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키워드

integral operatorbeamdeflectioneigenvalueL2-normelastic foundation
주제분류수학

초록

We provide a complete proof that there are no eigenvalues of the integral operator Kl outside the interval (0, 1/k). Kl 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.

Abstract

We provide a complete proof that there are no eigenvalues of the integral operator Kl outside the interval (0, 1/k). Kl 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.

참고문헌 (14)

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  3. 최성우, "SPECTRAL ANALYSIS OF THE INTEGRAL OPERATOR ARISING FROM THE BEAM DEFLECTION PROBLEM ON ELASTIC FOUNDATION I: POSITIVENESS AND CONTRACTIVENESS", Journal of Applied Mathematics and Informatics, 30(1), pp.27~47 (2012), 한국전산응용수학회
  4. S. W. Choi, "Spectral analysis of the integral operator arising from the beam deflection prob-lem on elastic foundation II: eigenvalues", Bound. Value Probl, 2015(6), pp.27~ (2015)
  5. S. W. Choi, "Existence and uniqueness of nonlinear deflections of an in-finite beam resting on a non-uniform nonlinear elastic foundation", Bound. Value Probl, 2012(5), pp.24~ (2012)
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  8. M. R. Grossinho, "Solvability of an elastic beam equation in presence of a sign-type Nagumo control", Nonlinear Stud, 18(2), pp.279~291 (2011)
  9. M. Hetenyi, "Beams on Elastic Foundation" (1946), The University of Michigan Press
  10. Y. H. Kuo, "Deflection of non-uniform beams resting on a nonlinear elastic foundation", Comput. Struct, 51, pp.513~519 (1994)
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