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Existence of positive solutions for nonlinear fractional systems in bounded domains

Keywords: Fractional nonlinear systems , Green function , positive solutions , blow-up solutions

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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 $mathbb{R}^n$ $(ngeq 3)$, subject to Dirichlet conditions, where $0

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