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

Li Chen; Yujuan Chen; Dang Luo

Annales Polonici Mathematici (2013)

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

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topLi 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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