Control and perturbation in Sturm — Liouville’s problem with discontinuous nonlinearity
We consider the Sturm — Liouville problem with discontinuous nonlinearity, control and perturbation. Previously obtained results for equations with a spectral parameter and a discontinuous operator are applied to this problem. By the variational method, we have established theorems on the existence...
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Veröffentlicht in: | Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes 2023, Vol.19 (2), p.275-282 |
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Hauptverfasser: | , |
Format: | Artikel |
Sprache: | eng ; rus |
Online-Zugang: | Volltext |
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Zusammenfassung: | We consider the Sturm — Liouville problem with discontinuous nonlinearity, control and perturbation. Previously obtained results for equations with a spectral parameter and a discontinuous operator are applied to this problem. By the variational method, we have established theorems on the existence of solutions to the Sturm — Liouville problem with discontinuous nonlinearity and to the optimal control problem, as well as on topological properties of the set of the acceptable “control — state” pairs. A one-dimensional analog of the Gol’dshtik model for separated flows of an incompressible fluid with control and perturbation is given as an application. |
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ISSN: | 1811-9905 2542-2251 |
DOI: | 10.21638/11701/spbu10.2023.212 |