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

L. M. Kozhevnikova; A. P. Kashnikova

Geodesic

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

L. M. Kozhevnikova ; A. P. Kashnikova

Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 2055-2067

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Résumé

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, Dirichlet problem, pseudomonotone operator, unbounded domain.
Mots-clés : $\Delta_2$-condition, existence of a solution

@article{SEMR_2020_17_a111,
     author = {L. M. Kozhevnikova and A. P. Kashnikova},
     title = {Existence of~a~solution to~a~nonlinear elliptic equation in {a~Musielak--Orlicz--Sobolev} space for~an~unbounded domain},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {2055--2067},
     publisher = {mathdoc},
     volume = {17},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2020_17_a111/}
}

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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. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 2055-2067. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a111/