Existence of Solutions of Anisotropic Elliptic Equations with Variable Indices of Nonlinearity in ℝⁿ

Abstract

In this paper, we consider a certain class of anisotropic second-order elliptic equations of divergent type with variable indices of nonlinearities. We examine conditions of the solvability in the whole space ℝn, n ≥ 2. We prove the existence of solutions without restrictions to the growth rate as |x| → ∞.