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

Abstract

© 2018, Pleiades Publishing, Ltd. 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| → ∞.