Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 208, pp. 1-11.

Title: Existence of positive solutions for nonlinear fractional systems
       in bounded domains
        
Author: Imed Bachar (King Saud Univ., Riyadh, Saudi Arabia)

Abstract:
 We prove the existence of positive continuous solutions to the nonlinear
 fractional system
 $$\displaylines{
 (-\Delta|_D) ^{\alpha/2}u+\lambda g(.,v) =0,  \cr
 (-\Delta|_D) ^{\alpha/2}v+\mu f(.,u)  =0,
 }$$
 in a bounded $C^{1,1}$-domain $D$ in $\mathbb{R}^n$ $(n\geq 3)$,
 subject to Dirichlet conditions, where $0<\alpha \leq 2$, $\lambda $
 and $\mu $ are nonnegative parameters. The functions f and g are
 nonnegative continuous monotone with respect to the second variable
 and satisfying certain  hypotheses related to the Kato class.

Submitted September 8, 2012. Published November 25, 2012.
Math Subject Classifications: 35J60, 34B27, 35B44.
Key Words: Fractional nonlinear systems; Green function; 
           positive solutions; blow-up solutions