Geodesic
Existence of solutions of anisotropic elliptic equations with variable indices of nonlinearity in $\mathbb{R}^n$
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences ICMMAS-17, St. Petersburg Polytechnic University, July 24-28, 2017, Tome 160 (2019), pp. 49-60.

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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 $|\mathrm{x}|\rightarrow \infty$.
Mots-clés : anisotropic elliptic equation, existence
Keywords: generalized solution, variable index of nonlinearity, $p(\mathrm{x})$-Laplacian. 
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     title = {Existence of solutions of anisotropic elliptic equations with variable indices of nonlinearity in $\mathbb{R}^n$},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
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L. M. Kozhevnikova; A. Sh. Kamalеtdinov. Existence of solutions of anisotropic elliptic equations with variable indices of nonlinearity in $\mathbb{R}^n$. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences ICMMAS-17, St. Petersburg Polytechnic University, July 24-28, 2017, Tome 160 (2019), pp. 49-60. http://geodesic.mathdoc.fr/item/INTO_2019_160_a6/

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