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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2020, Volume 17, Pages 2055–2067
DOI: https://doi.org/10.33048/semi.2020.17.137 (Mi semr1331) 		 
Differentical equations, dynamical systems and optimal control

Existence of a solution to a nonlinear elliptic equation in a Musielak–Orlicz–Sobolev space for an unbounded domain

L. M. Kozhevnikovaab, A. P. Kashnikovaa

a Sterlitamak Branch of Bashkir State University, 37, Lenin ave., Sterlitamak, 453103, Russia
b Elabuga Branch of Kazan (Volga Region) Federal University, 89, Kazanskaya str., Elabuga, 423600, Russia
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DOI: https://doi.org/10.33048/semi.2020.17.137
Abstract: We consider a class of second-order elliptic equations with nonlinearities defined by generalized $N$-functions. The existence of a weak solution to the Dirichlet problem in a reflexive Musielak–Orlicz–Sobolev space is proved for an arbitrary unbounded domain.
Keywords: Musielak–Orlicz-Sobolev space, $\Delta_2$-condition, Dirichlet problem, existence of a solution, pseudomonotone operator, unbounded domain.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00428
Supported by RFBR (Grant 18-01-00428).
Bibliographic databases:
Document Type: Article
UDC: 517.956.25
MSC: 35J20, 35J25, 35J62
Language: English
Citation: L. M. Kozhevnikova, A. P. Kashnikova, “Existence of a solution to a nonlinear elliptic equation in a Musielak–Orlicz–Sobolev space for an unbounded domain”, Sib. Èlektron. Mat. Izv., 17 (2020), 2055–2067
Citation in format AMSBIB
\Bibitem{KozKas20}
\by L.~M.~Kozhevnikova, A.~P.~Kashnikova
\paper Existence of~a~solution to~a~nonlinear elliptic equation in a~Musielak--Orlicz--Sobolev space for~an~unbounded domain
\jour Sib. \`Elektron. Mat. Izv.
\yr 2020
\vol 17
\pages 2055--2067
\mathnet{http://mi.mathnet.ru/semr1331}
\crossref{https://doi.org/10.33048/semi.2020.17.137}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000598535000001}
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