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Discontinuity, Nonlinearity, and Complexity 11(4) (2022) 757--765 | DOI:10.5890/DNC.2022.12.013

Sounia Zeditri, Kamel Akrout, Rafik Guefaifia

Laboratory of Mathematics, Informatics and Systems, Larbi Tebessi, University, Tebessa, 12000, Algeria

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Abstract

In this paper we consider following (p,q)-Laplacian system \begin{equation*} \left\{ \begin{split} & -\Delta _{p}u=\lambda l\left( x\right) u^{p-1}-f_{1}\left( u,v\right) -au^{-\alpha _{1}}v^{\beta _{2}}\ \text{in }\Omega , \\ & -\Delta _{q}v=\mu k\left( x\right) v^{q-1}-f_{2}\left( u,v\right) -bu^{\alpha _{2}}v^{-\beta _{2}}\text{ in }\Omega , \\ & u=v=0\text{ on }\partial \Omega ,% \end{split} \right. \end{equation*} where $\Omega $ is a bounded domain in $\mathbb{R}^{N}$ with smooth boundary $\partial \Omega $, $\lambda $ and $\mu $ are a positive parameters and $a,$ $b$ are a positive constant. By using the method of sub-supersolution we discuss the existence of positive solution.

Acknowledgments

The authors acknowledge to Prof. Salah Mahmoud Boulaaras from Qassim University at Saudi Arabia for a first revision and kind comments on this work. The authors would like to thank the anonymous referees and the handling editor for their careful reading and for relevant remarks/suggestions.

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