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Siberian Journal of Pure and Applied Mathematics, 2016, Volume 16, Issue 2, Pages 26–40
(Mi vngu400)
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This article is cited in 1 scientific paper (total in 1 paper)
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.
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
Linking options:
https://www.mathnet.ru/eng/vngu400 https://www.mathnet.ru/eng/vngu/v16/i2/p26
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Abstract page: | 239 | Full-text PDF : | 43 | References: | 37 | First page: | 11 |
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