Existence of solutions of anisotropic elliptic equations with variable indices of nonlinearity in $\mathbb{R}^n$

In this paper, we consider a certain class of anisotropic second-order elliptic equations of divergent type with variable indices of nonlinearity. We examine conditions of the solvability in the whole space $\mathbb{R}^n$, $n\geq 2$. We prove the existence of solutions without restrictions to the growth rate as $|\mathrm{x}|\rightarrow \infty$.