Geodesic
Control and perturbation in Sturm --- Liouville's problem with discontinuous nonlinearity
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 19 (2023) no. 2, pp. 275-282

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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.
Mots-clés : Sturm — Liouville's problem
Keywords: discontinuous nonlinearity, control problems, variational method, Gol'dshtik's model. 
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     author = {O. V. Baskov and D. K. Potapov},
     title = {Control and perturbation in {Sturm} --- {Liouville's} problem with discontinuous nonlinearity},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
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     volume = {19},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2023_19_2_a11/}
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O. V. Baskov; D. K. Potapov. Control and perturbation in Sturm --- Liouville's problem with discontinuous nonlinearity. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 19 (2023) no. 2, pp. 275-282. http://geodesic.mathdoc.fr/item/VSPUI_2023_19_2_a11/