We study periodic solutions to the problem for the quasilinear Euler–Bernoulli equation governed oscillations of an I-beam with the homogeneous boundary conditions corresponding to the hinged and fixed beam endpoints. We obtain an asymptotic formula for the eigenvalues of the Sturm–Liouville problem and prove the existence of infinitely many solutions provided that the nonlinear term has a power growth. Bibliography: 12 titles.
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Translated from Problemy Matematicheskogo Analiza 104, 2020, pp. 111-119.
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Rudakov, I.A. Periodic Solutions to Quasilinear Oscillation Equations for Cables and Beams. J Math Sci 250, 123–133 (2020). https://doi.org/10.1007/s10958-020-05004-8
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DOI: https://doi.org/10.1007/s10958-020-05004-8