In this work, we study the existence of positive solutions to the singular system$$\left\{\begin{array}{ll}-\Delta_{p}u = \lambda a(x)f(v)-u^{-\alpha} & \textrm{ in }\Omega,\\-\Delta_{p}v = \lambda b(x)g(u)-v^{-\alpha} & \textrm{ in }\Omega,\\u = v= 0 & \textrm{ on }\partial \Omega,\end{array}\right.$$where $\lambda $ is positive parameter, $\Delta_{p}u=\textrm{div}(|\nabla u|^{p-2} \nabla u)$, $p>1$, $ \Omega \subset R^{n} $ some for $ n >1 $, is a bounded domain with smooth boundary $\partial \Omega $ , $ 0<\alpha< 1 $, and $f,g: [0,\infty] \to\R$ are continuous, nondecreasing functions which are asymptotically $ p $-linear at $\infty$. We prove the existence of a positive solution for a certain range of $\lambda$ using the method of sub-supersolutions.
@article{31983,
title = {On the existence results for a class of singular elliptic system involving indefinite weight functions and asymptotically linear growth forcing term},
journal = {Boletim da Sociedade Paranaense de Matem\'atica},
volume = {37},
year = {2017},
doi = {10.5269/bspm.v37i3.31983},
language = {EN},
url = {http://dml.mathdoc.fr/item/31983}
}
Afrouzi, Ghasem A.; Shakeri, S.; Chung, N. T. On the existence results for a class of singular elliptic system involving indefinite weight functions and asymptotically linear growth forcing term. Boletim da Sociedade Paranaense de Matemática, Tome 37 (2017) . doi : 10.5269/bspm.v37i3.31983. http://gdmltest.u-ga.fr/item/31983/