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. Kozhevnikova^ab, A. P. Kashnikova<sup>a

a</sup> 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

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.

UDC: 517.956.25

MSC: 35J20, 35J25, 35J62

Language: English

DOI: 10.33048/semi.2020.17.137

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