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Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2019, Volume 160, Pages 49–60 (Mi into424)  

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

L. M. Kozhevnikovaab, A. Sh. Kamalåtdinova

a Sterlitamak Branch of Bashkir State University
b Elabuga Branch of Kazan (Volga Region) Federal University

Abstract: 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 $|\mathrm{x}|\rightarrow \infty$.

Keywords: anisotropic elliptic equation, existence, generalized solution, variable index of nonlinearity, $p(\mathrm{x})$-Laplacian

Funding Agency Grant Number
Russian Foundation for Basic Research 18-01-00428_a
This work was supported by the Russian Foundation for Basic Research (project No. 18-01-00428).


Full text: PDF file (284 kB)
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UDC: 517.956.25
MSC: 35J25, 35J62, 35D30

Citation: L. M. Kozhevnikova, A. Sh. Kamalåtdinov, “Existence of solutions of anisotropic elliptic equations with variable indices of nonlinearity in $\mathbb{R}^n$”, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences ICMMAS-17, St. Petersburg Polytechnic University, July 24-28, 2017, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 160, VINITI, Moscow, 2019, 49–60

Citation in format AMSBIB
\Bibitem{KozKam19}
\by L.~M.~Kozhevnikova, A.~Sh.~Kamalåtdinov
\paper Existence of solutions of anisotropic elliptic equations with variable indices of nonlinearity in $\mathbb{R}^n$
\inbook Proceedings of the International Conference on Mathematical Modelling in Applied Sciences ICMMAS-17,
St. Petersburg Polytechnic University, July 24-28, 2017
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz.
\yr 2019
\vol 160
\pages 49--60
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into424}


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