# Article

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Keywords:
Eigenvalue problem; Degenerate elliptic operator; Nonlinear systems; Positive solutions.
Summary:
In this paper, we consider the existence and nonexistence of positive solutions of degenerate elliptic systems $\left\rbrace \begin{array}{ll}-\Delta _p u = f(x,u,v), &\quad \text{in} \ \Omega , -\Delta _p v = g(x,u,v), &\quad \text{in} \ \Omega , u = v = 0, &\quad \text{on} \ \partial \Omega , \end{array}\right.$ where $-\Delta _p$ is the $p$-Laplace operator, $p>1$ and $\Omega$ is a $C^{1,\alpha }$-domain in $\mathbb R^n$. We prove an analogue of [7, 16] for the eigenvalue problem with $f(x,u,v)=\lambda _1 v^{p-1}$, $g(x,u,v)=\lambda _2u^{p-1}$ and obtain a non-existence result of positive solutions for the general systems.
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