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Approximation to the Sturm–Liouville Problem with a Discontinuous Nonlinearity

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Abstract

We consider a continuous approximation to the Sturm–Liouville problem with a nonlinearity discontinuous in the phase variable. The approximating problem is obtained from the original one by small perturbations of the spectral parameter and by approximating the nonlinearity by Carathéodory functions. The variational method is used to prove the theorem on the proximity of solutions of the approximating and original problems. The resulting theorem is applied to the one-dimensional Gol’dshtik and Lavrent’ev models of separated flows.

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Funding

This work was financially supported by the Russian Science Foundation, project 23-21-00069, https://rscf.ru/en/project/23-21-00069/.

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Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, 199034, Russia

    D. K. Potapov

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  1. D. K. Potapov
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Correspondence to D. K. Potapov.

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Translated by V. Potapchouck

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Potapov, D.K. Approximation to the Sturm–Liouville Problem with a Discontinuous Nonlinearity. Diff Equat 59, 1185–1192 (2023). https://doi.org/10.1134/S0012266123090045

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  • DOI: https://doi.org/10.1134/S0012266123090045

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