IJPAM: Volume 97, No. 3 (2014)

EXISTENCE OF WEAK POSITIVE SOLUTION FOR
CLASS OF $\left(p_{1},p_{2,...,}p_{n}\right) $-LAPLACIAN
ELLIPTIC SYSTEM WITH DIFFERENT WEIGHTS

Rafik Guefaifia$^1$, Kamel Akrout$^2$, Tahar Bouali$^3$
$^{1,2,3}$Department of Mathematics
University Badji Mokhtar
Annaba, 23000, ALGERIA


Abstract. Consider the system \begin{equation*} \left\{ \begin{array}{c} -\Delta _{P_{1},p_{1}}u_{1}=\lamb... ... on }\partial \Omega ,\quad i=1,2,...n,% \end{array}% \right. \end{equation*} where $ \Delta _{R_{i},r_{i}} $ with $ r_{i}>1 $ and $ R_{i}=R_{i}\left( x\right) $ is a weights functions, denotes the weighted $ r_{i} $ -Laplacian defined by $ % \Delta _{R_{i},r_{i}}u_{i}=\text{\rm div}\left( R_{i}\left( x\right) \left\vert \nabla u_{i}\right\vert ^{r_{i}-2}\nabla u_{i}\right) ,i=1,2,...n,\lambda $ is a positive parameter, $ a_{i}\left( x\right) $ , $ i=1,2,...n, $ are a weights functions,and $ \Omega $ is a bounded domain in $ \mathbb{R}^{N} $ $ \left( N>1\right) $ with smooth boundary $ \partial \Omega . $ We prove the existence of a large positive solutions for $ \lambda $ large, we use the method of sub-supersolutions to establish our results.

Received: May 23, 2014

AMS Subject Classification: 05C38, 15A15, 05A15, 15A18

Key Words and Phrases: positive solutions, sub-supersolutions, p-Laplacian systems

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DOI: 10.12732/ijpam.v97i3.4 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 97
Issue: 3
Pages: 303 - 310


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