Boundary blow-up solutions for a cooperative system involving the $p$-Laplacian
Annales Polonici Mathematici, Tome 109 (2013) no. 3, pp. 297-310
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
We study necessary and sufficient conditions for the existence of nonnegative boundary blow-up solutions to the cooperative system $\varDelta _p u=g(u-\alpha v),$ $\varDelta _p v=f(v-\beta u)$ in a smooth bounded domain of $\mathbb {R}^N$, where $\varDelta _p$ is the $p$-Laplacian operator defined by $\varDelta _p u = {\rm div}(|\nabla u|^{p-2}\nabla u)$ with $p >1$, $f$ and $g$ are nondecreasing, nonnegative $C^1$ functions, and $\alpha $ and $\beta $ are two positive parameters. The asymptotic behavior of solutions near the boundary is obtained and we get a uniqueness result for $p=2$.
Keywords:
study necessary sufficient conditions existence nonnegative boundary blow up solutions cooperative system vardelta u alpha vardelta v beta smooth bounded domain mathbb where vardelta p laplacian operator defined vardelta div nabla p nabla nondecreasing nonnegative functions alpha beta positive parameters asymptotic behavior solutions near boundary obtained get uniqueness result
Affiliations des auteurs :
Li Chen 1 ; Yujuan Chen 1 ; Dang Luo 2
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author = {Li Chen and Yujuan Chen and Dang Luo},
title = {Boundary blow-up solutions for a cooperative system involving the $p${-Laplacian}},
journal = {Annales Polonici Mathematici},
pages = {297--310},
publisher = {mathdoc},
volume = {109},
number = {3},
year = {2013},
doi = {10.4064/ap109-3-5},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ap109-3-5/}
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%0 Journal Article %A Li Chen %A Yujuan Chen %A Dang Luo %T Boundary blow-up solutions for a cooperative system involving the $p$-Laplacian %J Annales Polonici Mathematici %D 2013 %P 297-310 %V 109 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/ap109-3-5/ %R 10.4064/ap109-3-5 %G en %F 10_4064_ap109_3_5
Li Chen; Yujuan Chen; Dang Luo. Boundary blow-up solutions for a cooperative system involving the $p$-Laplacian. Annales Polonici Mathematici, Tome 109 (2013) no. 3, pp. 297-310. doi: 10.4064/ap109-3-5
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