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Title: | Symmetry and monotonicity results for positive solutions of p-Laplace systems | Authors: | Azizieh, Céline | Keywords: | p-Laplacian; symmetry results; systems 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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