ISSN 2234-8417 (Online) ISSN 1598-5857 (Print)

 2017's 35, 1-2(Jan)

 POSITIVE SOLUTION FOR A CLASS OF NONLOCAL ELLIPTIC SYSTEM WITH MULTIPLE PARAMETERS AND SINGULAR WEIGHTS By G.A. AFROUZI ..........1702

Generic Number - 1702
References - 27
Written Date - January 17th, 17
Modified Date - January 17th, 17
 Summary This study is concerned with the existence of positive solution for the following nonlinear elliptic system \begin{eqnarray*} \begin{cases}-M_1\left(\int_\Omega |x|^{-ap}|\nabla u|^{p}\,dx\right) div(|x|^{-ap}|\nabla u|^{p-2}\nabla u)\\ \qquad \qquad \qquad\quad=|x|^{-(a+1)p+c_{1}}\Big(\alpha_{1}A_1(x)f(v)+\beta_{1}B_1(x)h(u)\Big),~~~x\in \Omega,\\ -M_2\left(\int_\Omega |x|^{-bq}|\nabla v|^{q}\,dx\right) \,div(|x|^{-bq}|\nabla v|^{q-2}\nabla v\,)\,\\ \qquad \qquad \qquad\quad=|x|^{-(b+1)q+c_{2}}\Big(\alpha_{2}A_2(x)g(u)+\beta_{2}B_2(x)k(v)\Big),~~~x\in \Omega,\\ \quad u=v=0,\quad x\in \partial \Omega, \end{cases}\end{eqnarray*}where $\Omega$ is a bounded smooth domain of $\mathbb{R}^{N}$ with \$0\in \Omega,~1 Our approach is based on the sub and super solutions method