Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/4197
Title: Symmetry and monotonicity results for positive solutions of p-Laplace systems
Authors: Azizieh, Céline
Keywords: p-Laplaciansymmetry resultssystems of PDE's
Issue Date: 2002
Publisher: Università degli Studi di Trieste. Dipartimento di Scienze Matematiche
Source: Céline Azizieh, "Symmetry and monotonicity results for positive solutions of p-Laplace systems ", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 34 (2002), pp. 67-98.
Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
34 (2002)
Abstract: 
In this paper, we extend to a system of the type
\[
\begin{cases}
\begin{array}{c}
-\Delta_{p_{1}}u=f\left(v\right)\quad in\,\Omega,\quad u>0\quad in\,\Omega\quad u=0\quad on\,\partial\Omega,\\
-\Delta_{p_{2}}v=g\left(u\right)\quad in\,\Omega,\quad v>0\quad in\,\Omega\quad v=0\quad on\,\partial\Omega,
\end{array}\end{cases}
\]
where $\Omega\subset\mathbb{R}^{N}$ is bounded, the monotonicity
and simmetry results of Damascelli and Pacella obtained in $\left[5\right]$
in the case of a scalar p-Laplace equation with 1 < p < 2. For this
purpose, we use the moving hyperplanes method and we suppose that
$f,g\::\:\mathbb{R}\rightarrow\mathbb{R}^{+}$ are increasing on $\mathbb{R}^{+}$
and locally Lipschitz continuous on $\mathbb{R}$ and p$_{1},$ p$_{2}$
$\epsilon$ (1, 2) or p$_{1}\:\epsilon\left(1,\infty\right),$ p$_{2}$=2
Type: Article
URI: http://hdl.handle.net/10077/4197
ISSN: 0049-4704
Appears in Collections:Rendiconti dell'Istituto di matematica dell'Università di Trieste: an International Journal of Mathematics vol.34 (2002)

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