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Regular solutions of elliptic boundary-value problems with discontinuous nonlinearities


Authors: M. G. Lepchinskii and V. N. Pavlenko
Translated by: I. V. Denisova
Original publication: Algebra i Analiz, tom 17 (2005), nomer 3.
Journal: St. Petersburg Math. J. 17 (2006), 465-475
MSC (2000): Primary 35J65, 35J50
DOI: https://doi.org/10.1090/S1061-0022-06-00915-0
Published electronically: March 9, 2006
MathSciNet review: 2167847
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Abstract: The existence of stable solutions to elliptic boundary-value problems is studied; stability is understood with respect to perturbations of nonlinearities. By the variational method, it is shown that stable solutions of such problems do exist provided a certain integral measure of closeness for (possibly, discontinuous) nonlinearities is employed. It is shown that problems with discontinuous nonlinearities can serve as idealization of problems with continuous nonlinearities but having narrow regions of ill-controlled variations with respect to the phase variable.


References [Enhancements On Off] (What's this?)

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Additional Information

M. G. Lepchinskii
Affiliation: Numerical Mathematics Department, Chelyabinsk State University, Brat’ev Kashirinykh Street 129, Chelyabinsk 454021, Russia
Email: myth@csu.ru

V. N. Pavlenko
Affiliation: Numerical Mathematics Department, Chelyabinsk State University, Brat’ev Kashirinykh Street 129, Chelyabinsk 454021, Russia

DOI: https://doi.org/10.1090/S1061-0022-06-00915-0
Keywords: Elliptic boundary-value problems, discontinuous nonlinearities, strong solutions, $\mathrm{nl}$-stable solutions
Received by editor(s): May 26, 2005
Published electronically: March 9, 2006
Article copyright: © Copyright 2006 American Mathematical Society

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