Email this article Existence of Solutions of Anisotropic Elliptic Equations with Variable Exponents in Unbounded Domains
- Authors: Kamaletdinov A.S.1, Kozhevnikova L.M.1,2, Melnik L.Y.3
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Affiliations:
- Sterlitamak Branch of Bashkir State University
- Elabuga Branch of Kazan (Volga Region) Federal University
- Bashkir State Agrarian University
- Issue: Vol 39, No 2 (2018)
- Pages: 224-235
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/201464
- DOI: https://doi.org/10.1134/S1995080218020166
- ID: 201464
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Abstract
We consider a class of anisotropic elliptic differential equations of second order with divergent form and variable exponents. The corresponding elliptic operators are pseudo-monotone and coercive. We obtain solvability conditions for the Dirichlet problem in unbounded domains Ω ⊂ ℝn, n ≥ 2. The proof of existence of solutions is free of restrictions on growth of data for |x| → ∞.
About the authors
A. Sh. Kamaletdinov
Sterlitamak Branch of Bashkir State University
Author for correspondence.
Email: kamaletdinov-aleksandr@mail.ru
Russian Federation, pr. Lenina 37, Sterlitamak, 453103
L. M. Kozhevnikova
Sterlitamak Branch of Bashkir State University; Elabuga Branch of Kazan (Volga Region) Federal University
Email: kamaletdinov-aleksandr@mail.ru
Russian Federation, pr. Lenina 37, Sterlitamak, 453103; ul. Kazanskaya 89, Elabuga, Tatarstan, 423600
L. Yu. Melnik
Bashkir State Agrarian University
Email: kamaletdinov-aleksandr@mail.ru
Russian Federation, ul. 50 Let Oktyabrya 34, Ufa, 450001
