Commun. Korean Math. Soc. 2012; 27(3): 557-564
Printed September 1, 2012
https://doi.org/10.4134/CKMS.2012.27.3.557
Copyright © The Korean Mathematical Society.
S. H. Rasouli
Babol University of Technology
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
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd