Existence of Positive Solutions for a Class of Nonlocal Elliptic Systems With Multiple Parameters

Nguyen Thanh Chung, Ghasem Alizadeh Afrouzi

In this paper, we study the existence of positive solutions to the following nonlocal elliptic systems $$ \cases - M_1eft(ıt_mega |abla u|^p\,dx\right)\Delta_p u = lpha_1 a(x)f_1(v) + \beta_1b(x)g_1(u), \quad x ı mega, - M_2eft(ıt_mega |abla v|^q\,dx\right)\Delta_q v = lpha_2 c(x)f_2(u) + \beta_2d(x)g_2(v), \quad x ı mega, u = v = 0, \quad x ı tialmega, \endcases $$ where $\Omega$ is a bounded domain in $\Bbb{R}^N$ with smooth boundary $\partial\Omega$, $1<p,q<N$, $M_i : \Bbb{R}^+_0 \to \Bbb{R}$, $i=1,2$, are continuous and nondecreasing functions, $a,b,c,d \in C(\overline\Omega)$, and $\alpha_i$, $\beta_i$, $i=1,2$, are positive parameters.