Existence of solution to nonlinear elliptic equation in the Musielak-Orlicz-Sobolev space in unbounded domain

Authors

  • Larisa Kozhevnikova Sterlitamak Branch of Bashkir State University, Elabuga Branch of Kazan (Volga Region) Federal University
  • Anastasiya Kashnikova Sterlitamak Branch of Bashkir State University

Keywords:

Musielak-Orlicz-Sobolev spaces, $\Delta_2$-condition, Dirichlet problem, existence solution, pseudomonotone operator, unbounded domain.

Abstract

A class of second-order elliptic equations with non-linearities determined by generalized $N$ -functions is considered. In the reflective space of Muzilak-Orlicz-Sobolev, the existence of a weak solution of the Dirichlet problem in an arbitrary unbounded domain is proved.

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Published

2020-12-11

Issue

Vol. 17 (2020)

Section

Differential equations, dynamical systems and optimal control