On the existence of positive solution for a class of nonlinear elliptic system with multiple parameters and singular weights
Commun. Korean Math. Soc. 2012 Vol. 27, No. 3, 557-564
https://doi.org/10.4134/CKMS.2012.27.3.557
Printed September 1, 2012
S. H. Rasouli
Babol University of Technology
Abstract : This study concerns the existence of positive solution for the following nonlinear system $$ \left\{\begin{array}{ll} -div(|x|^{-ap}\,|\nabla u|^{p-2}\,\nabla u) = |x|^{-(a+1)p+c_{1}}\,(\alpha_{1} f(v)+\beta_{1} h(u)), x\in \Omega,\\ -div(|x|^{-bq}\,|\nabla v|^{q-2}\,\nabla v) = |x|^{-(b+1)q+c_{2}}\,(\alpha_{2} g(u)+\beta_{2} k(v)), x\in \Omega,\\ u = v = 0, x\in\partial \Omega, \end{array}\right. $$ where $\Omega$ is a bounded smooth domain of $\mathbb{R}^N$ with $0\in \Omega,$ $1
Keywords : singular weights, nonlinear elliptic system, multiple parameters
MSC numbers : 35J55, 35J65
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