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