Abstract
Under the Keller–Osserman condition on \({\Sigma_{j=1}^{2}f_{j}}\), we show the existence of entire positive solutions for the semilinear elliptic system \({\Delta u_{1}+|\nabla u_{1}|=p_{1}(x)f_{1}(u_{1},u_{2}), \Delta u_{2}+|\nabla u_{2}|=p_{2}(x)f_{2}(u_{1},u_{2}),x \in \mathbb{R}^{N}}\), where \({p_{j}(j=1, 2):\mathbb{R}^{N} \rightarrow [0,\infty)}\) are continuous functions.
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Jiang, X., Lv, X. Existence of entire positive solutions for semilinear elliptic systems with gradient term. Arch. Math. 99, 169–178 (2012). https://doi.org/10.1007/s00013-012-0414-y
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DOI: https://doi.org/10.1007/s00013-012-0414-y