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

L. M. Kozhevnikova   ; A. A. Nikitina

Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 16 (2016) no. 2, pp. 26-40

Résumé

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.

Détail

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

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