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Positive radial solutions for some quasilinear elliptic systems in exterior domains

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  • We use fixed-point theorem of cone expansion/compression type to prove the existence of positive radial solutions for the following class of quasilinear elliptic systems in exterior domains

    $-\Delta_p u = k_1(|x| )f(u,v),$ for $|x| > 1$ and $x \in \mathbb R^N, $

    $-\Delta_p v = k_2(|x|)g(u,v),$ for $|x| > 1 $ and $x \in \mathbb R^N, $

    $u(x) = v(x) =0,$ for $|x| =1, $

    $u(x), v(x) \rightarrow 0 $ as $|x| \rightarrow +\infty,$

    where $1 < p < N $ and $\Delta_p u=$ div $(|\nabla u|^{p-2}\nabla u )$ is the p-Laplacian operator. We consider nonlinearities that are either superlinear or sublinear.

    Mathematics Subject Classification: Primary: 35J55, 34B15; Secondary: 34B18.

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