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This article is cited in 3 scientific papers (total in 3 papers)
Existence of Semiregular Solutions of Elliptic Systems with Discontinuous Nonlinearities
V. N. Pavlenkoa, D. K. Potapovb a Chelyabinsk State University
b Saint Petersburg State University
Abstract:
For elliptic systems with discontinuous nonlinearities, we study the existence of strong solutions whose values are points of continuity with respect to the state variables for almost all values of the spatial variable. Such solutions are said to be semiregular. An upper-and-lower-solution principle is established for the existence of semiregular solutions to elliptic systems with discontinuous nonlinearities. This principle is used to prove theorems on the existence of semiregular solutions of elliptic systems with discontinuous nonlinearities, in particular, nontrivial solutions of problems with a parameter. Examples of classes of nonlinearities with separated variables satisfying the conditions of our theorems are given.
Keywords:
elliptic system, discontinuous nonlinearity, semiregular solution, upper solution, lower solution.
Received: 15.10.2019 Revised: 19.03.2021
Citation:
V. N. Pavlenko, D. K. Potapov, “Existence of Semiregular Solutions of Elliptic Systems with Discontinuous Nonlinearities”, Mat. Zametki, 110:2 (2021), 239–257; Math. Notes, 110:2 (2021), 226–241
Linking options:
https://www.mathnet.ru/eng/mzm12596https://doi.org/10.4213/mzm12596 https://www.mathnet.ru/eng/mzm/v110/i2/p239
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Abstract page: | 214 | Full-text PDF : | 59 | References: | 36 | First page: | 8 |
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