Electronic Journal of Differential Equations

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

Existence of positive solutions for nonlinear fractional systems in bounded domains
Imed Bachar

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

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	Imed Bachar King Saud University College of Science Mathematics Department P.O. Box 2455 Riyadh 11451 Kingdom of Saudi Arabia email: abachar@ksu.edu.sa

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Existence of positive solutions for nonlinear fractional systems in bounded domains Imed Bachar

Existence of positive solutions for nonlinear fractional systems in bounded domains
Imed Bachar