Existence of entire positive solutions for semilinear elliptic systems with gradient term |
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Authors: | Xiaowei Jiang Xuezhe Lv |
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Institution: | 1. College of Mathematics, Beihua University, Jilin, 132013, China
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Abstract: | Under the Keller?COsserman 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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