| Abstract: |
| The main goal of this work is to study existence$\backslash$non-existence of non-negative super-solution to a class of gradients-potential systems with Hardy term. More precisely, we consider the system
$\begin{equation*}
\tag{$\mathbf{S}_\lambda$}\qquad\left\{
\begin{array}{rcll}
-\Delta u-\l\dfrac{u}{|x|^2}& = & f_1(x,v, \nabla v) & \text{in }\Omega , \
-\Delta v-\l\dfrac{v}{|x|^2}& = &f_2(x,u,\nabla u) &\text{in }\Omega , \
u=v&=& 0 & \text{on }\partial \Omega,
\end{array}\right.
\end{equation*}$
where $\Omega \subset \mathbb{R}^N, N\ge 3, $ is a bounded regular domain such that $0\in\Omega$. Here, $01$, we prove the existence of an optimal critical curve in the $(p,\,q)$-plane, that separates the existence and non-existence regions. |
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