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Sib. J. Pure and Appl. Math., 2016, Volume 16, Issue 2, Pages 26–40 (Mi vngu400)  

Qualitative properties of solutions of elliptic equations with non-power nonlinearities in $\mathbb{R}_n$

L. M. Kozhevnikovaa, A. A. Nikitinab

a Sterlitamak Branch of Bashkir State University
b Tyumen State University

Abstract: Some class of anisotropic elliptic equations with non-power nonlinearities in space $\mathbb{R}_n$ is considered
$$ -\sum\limits_{\alpha=1}^{n}(a_{\alpha}(\mathrm{x},u_{x_{\alpha}}))_{x_{\alpha}}+a_0(\mathrm{x},u)=F_0( \mathrm{x}).$$
The theorem of existence of solutions in local Sobolev–Orlicz spaces without restrictions on data growth on infinity is proved. Conditions on structure of an equation, sufficient for uniqueness of solutions, without restrictions on its growth on infinity are found. The power estimate characterizing the behavior of the solution at infinity is installed. The continuous dependence of solution on right side of solution is proved.

Keywords: anisotropic elliptic equations, nonpower nonlinearity, Sobolev–Orlicz space, unbounded domains.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-31-50034_мол_нр


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English version:
Journal of Mathematical Sciences, 2018, 228:4, 395–408

UDC: 517.956.25
Received: 25.12.2015

Citation: L. M. Kozhevnikova, A. A. Nikitina, “Qualitative properties of solutions of elliptic equations with non-power nonlinearities in $\mathbb{R}_n$”, Sib. J. Pure and Appl. Math., 16:2 (2016), 26–40; J. Math. Sci., 228:4 (2018), 395–408

Citation in format AMSBIB
\Bibitem{KozNik16}
\by L.~M.~Kozhevnikova, A.~A.~Nikitina
\paper Qualitative properties of solutions of elliptic equations with non-power nonlinearities in $\mathbb{R}_n$
\jour Sib. J. Pure and Appl. Math.
\yr 2016
\vol 16
\issue 2
\pages 26--40
\mathnet{http://mi.mathnet.ru/vngu400}
\transl
\jour J. Math. Sci.
\yr 2018
\vol 228
\issue 4
\pages 395--408
\crossref{https://doi.org/10.1007/s10958-017-3630-y}


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