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Symmetry and monotonicity results for positive solutions of p-Laplace systems
Azizieh, Céline
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
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
34 (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.
Languages
en
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