Boundary blow-up solutions for a cooperative system involving the p-Laplacian

Li Chen; Yujuan Chen; Dang Luo

Li Chen ; Yujuan Chen ; Dang Luo

Annales Polonici Mathematici, Tome 107 (2013), p. 297-310 / Harvested from The Polish Digital Mathematics Library

Résumé

We study necessary and sufficient conditions for the existence of nonnegative boundary blow-up solutions to the cooperative system $Δ_{p} u = g (u - α v), Δ_{p} v = f (v - β u)$ in a smooth bounded domain of $ℝ^{N}$ , where $Δ_{p}$ is the p-Laplacian operator defined by $Δ_{p} u = {d i v (| \nabla u |}^{p - 2} \nabla u)$ with p > 1, f and g are nondecreasing, nonnegative C¹ functions, and α and β are two positive parameters. The asymptotic behavior of solutions near the boundary is obtained and we get a uniqueness result for p = 2.

Publié le : 2013-01-01

Zbl 1311.35108

EUDML-ID : urn:eudml:doc:280190

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     title = {Boundary blow-up solutions for a cooperative system involving the p-Laplacian},
     journal = {Annales Polonici Mathematici},
     volume = {107},
     year = {2013},
     pages = {297-310},
     zbl = {1311.35108},
     language = {en},
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Li Chen; Yujuan Chen; Dang Luo. Boundary blow-up solutions for a cooperative system involving the p-Laplacian. Annales Polonici Mathematici, Tome 107 (2013) pp. 297-310. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap109-3-5/