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A generalized solution in W2 1(0,1) of a problem concerning the deflection of a beam

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Abstract

A new method is proposed for formulating a boundary-value problem for a fourth-order ordinary differential equation with a solution in W2 1(0, 1). This generalized formulation is based on a system of second-order equations with coefficients in W2 −1 (0, 1). The existence and uniqueness of the indicated solution in this class is proven.

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Literature cited

  1. N. M. Belyaev, Strength of Materials [in Russian], Moscow (1976).

  2. Yu. M. Berezanskii, Eigenfunction Expansions of Self-Adjoint Operators [in Russian], Kiev (1965).

  3. V. S. Vladimirov, Equations of Mathematical Physics [in Russian], Moscow (1971).

  4. I. I. Lyashko, V. P. Dudenko, and O. E. Tsitritskii, Acoustic Filtration [in Russian], Kiev (1979).

  5. K. Rektorys, Variational Methods in Mathematics, Science, and Engineering [Russian translation], Moscow (1985).

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Authors and Affiliations

  1. Kiev State University, Kiev

    I. V. Karnaukh

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  1. I. V. Karnaukh
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Additional information

Translated fromVychislitel'naya i Prikladnaya Matematika, No. 69, pp. 90–96, 1989.

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Karnaukh, I.V. A generalized solution in W2 1(0,1) of a problem concerning the deflection of a beam. J Math Sci 67, 3104–3108 (1993). https://doi.org/10.1007/BF01098148

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  • DOI: https://doi.org/10.1007/BF01098148

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