1Department of Mathematics Nantong University 226007, Nantong, P.R. China 2College 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
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
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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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},
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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
