Abstract

In this paper, we study the existence of positive solutions to the following nonlocal elliptic systems $$ \cases - M_1\left(\int_\Omega |\nabla u|^p\,dx\right)\Delta_p u = \alpha_1 a(x)f_1(v) + \beta_1b(x)g_1(u), \quad x \in \Omega,\\ - M_2\left(\int_\Omega |\nabla v|^q\,dx\right)\Delta_q v = \alpha_2 c(x)f_2(u) + \beta_2d(x)g_2(v), \quad x \in \Omega,\\ u = v = 0, \quad x \in \partial\Omega, \endcases $$ where $\Omega$ is a bounded domain in $\Bbb{R}^N$ with smooth boundary $\partial\Omega$, $1

Keywords: Nonlocal elliptic systems; positive solutions; sub and supersolutions method.

MSC: 35D05, 35J60

Pages:  166$-$173     

Volume  67 ,  Issue  3 ,  2015