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

 
 
 
   
 
Table of Contents
   
 
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
Downloaded Counts - 43
Visited Counts - 184
 
Original File
 
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
 
 
   
 
   

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