MATEMATIČKI VESNIK
МАТЕМАТИЧКИ ВЕСНИК



MATEMATIČKI VESNIK
Existence of positive solutions for a class of nonlocal elliptic systems with multiple parameters
Nguyen Thanh Chung and Ghasem Alizadeh Afrouzi

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

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

MSC: 35D05, 35J60

Pages:  166--173     

Volume  67 ,  Issue  3 ,  2015