Lobachevskii Journal of Mathematics

, Volume 39, Issue 2, pp 224–235 | Cite as

Existence of Solutions of Anisotropic Elliptic Equations with Variable Exponents in Unbounded Domains

  • A. Sh. Kamaletdinov
  • L. M. Kozhevnikova
  • L. Yu. Melnik


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| → ∞.

Keywords and phrases

anisotropic elliptic equation existence solution variable exponent Dirichlet problem pseudomonotone operator 


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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • A. Sh. Kamaletdinov
    • 1
  • L. M. Kozhevnikova
    • 1
    • 2
  • L. Yu. Melnik
    • 3
  1. 1.Sterlitamak Branch of Bashkir State UniversitySterlitamakRussia
  2. 2.Elabuga Branch of Kazan (Volga Region) Federal UniversityElabuga, TatarstanRussia
  3. 3.Bashkir State Agrarian UniversityUfaRussia

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