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

• Volume: 109, Issue: 3, page 297-310
• ISSN: 0066-2216

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## Abstract

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We study necessary and sufficient conditions for the existence of nonnegative boundary blow-up solutions to the cooperative system ${\Delta }_{p}u=g\left(u-\alpha v\right),{\Delta }_{p}v=f\left(v-\beta u\right)$ in a smooth bounded domain of ${ℝ}^{N}$, where ${\Delta }_{p}$ is the p-Laplacian operator defined by ${\Delta }_{p}u={div\left(|\nabla u|}^{p-2}\nabla u\right)$ 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.

## How to cite

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Li Chen, Yujuan Chen, and Dang Luo. "Boundary blow-up solutions for a cooperative system involving the p-Laplacian." Annales Polonici Mathematici 109.3 (2013): 297-310. <http://eudml.org/doc/280190>.

@article{LiChen2013,
abstract = {We study necessary and sufficient conditions for the existence of nonnegative boundary blow-up solutions to the cooperative system $Δ_p u = g(u-αv), Δ_p v = f(v-βu)$ in a smooth bounded domain of $ℝ^N$, where $Δ_p$ is the p-Laplacian operator defined by $Δ_p u = div(|∇u|^\{p-2\} ∇u)$ 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.},
author = {Li Chen, Yujuan Chen, Dang Luo},
journal = {Annales Polonici Mathematici},
keywords = {large solutions; boundary blow-up; cooperative; quasilinear elliptic system},
language = {eng},
number = {3},
pages = {297-310},
title = {Boundary blow-up solutions for a cooperative system involving the p-Laplacian},
url = {http://eudml.org/doc/280190},
volume = {109},
year = {2013},
}

TY - JOUR
AU - Li Chen
AU - Yujuan Chen
AU - Dang Luo
TI - Boundary blow-up solutions for a cooperative system involving the p-Laplacian
JO - Annales Polonici Mathematici
PY - 2013
VL - 109
IS - 3
SP - 297
EP - 310
AB - We study necessary and sufficient conditions for the existence of nonnegative boundary blow-up solutions to the cooperative system $Δ_p u = g(u-αv), Δ_p v = f(v-βu)$ in a smooth bounded domain of $ℝ^N$, where $Δ_p$ is the p-Laplacian operator defined by $Δ_p u = div(|∇u|^{p-2} ∇u)$ 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.
LA - eng
KW - large solutions; boundary blow-up; cooperative; quasilinear elliptic system
UR - http://eudml.org/doc/280190
ER -

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