| Volume 10, Number 4, 2020, Pages 1311-1325 DOI：10.11948/20190189 |
| Uniqueness and existence of solutions for a singular system with nonlocal operator via perturbation method |
| Kamel Saoudi,Mouna Kratou,Eadah AlZahrani |
| Keywords:Singular nonlocal elliptic system, approximated methods, variationals methods, existence of solutions, uniqueness of solutions. |
| Abstract: |
| In this work, we investigate the existence and the uniqueness of solutions for the nonlocal elliptic system involving a singular nonlinearity as follows:
$$
\left\{\begin{array}{ll}
(-\Delta_p)^su = a(x)|u|^{q-2}u +\frac{1-\alpha}{2-\alpha-\beta} c(x)|u|^{-\alpha}|v|^{1-\beta}, \quad
\text{in }\Omega,\ (-\Delta_p)^s v= b(x)|v|^{q-2}v +\frac{1-\beta}{2-\alpha-\beta} c(x)|u|^{1-\alpha}|v|^{-\beta}, \quad
\text{in }\Omega,\ u=v
= 0 ,\;\;\mbox{ in }\,\mathbb{R}^N\setminus\Omega,
\end{array}
\right.
$$
where $\Omega $ is a bounded domain in $\mathbb{R}^{n}$ with smooth boundary, $0<\alpha <1,$ $0<\beta <1,$ $2-\alpha -\beta |
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