Geodesic
Boundary blow-up solutions for a cooperative system involving the $p$-Laplacian
Li Chen1 ; Yujuan Chen1 ; Dang Luo2
1 Department of Mathematics Nantong University 226007, Nantong, P.R. China
2 College of Mathematics and Information Science North China University of Water Resources and Electric Power 450011, Zhengzhou, P.R. China
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 $p=2$.
DOI : 10.4064/ap109-3-5
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

Li Chen 1 ; Yujuan Chen 1 ; Dang Luo 2

1 Department of Mathematics Nantong University 226007, Nantong, P.R. China
2 College of Mathematics and Information Science North China University of Water Resources and Electric Power 450011, Zhengzhou, P.R. China 
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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 109 (2013) no. 3, pp. 297-310. doi : 10.4064/ap109-3-5. http://geodesic.mathdoc.fr/articles/10.4064/ap109-3-5/

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