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 ⊂ ℝ n , n ≥ 2. The proof of existence of solutions is free of restrictions on growth of data for |x| → ∞.
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Kamaletdinov, A.S., Kozhevnikova, L.M. & Melnik, L.Y. Existence of Solutions of Anisotropic Elliptic Equations with Variable Exponents in Unbounded Domains. Lobachevskii J Math 39, 224–235 (2018). https://doi.org/10.1134/S1995080218020166
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DOI: https://doi.org/10.1134/S1995080218020166