Year: 2014
Author: Kamel Akrout, Rafik Guefaifia
Journal of Partial Differential Equations, Vol. 27 (2014), Iss. 2 : pp. 158–165
Abstract
In this work, we are interested to obtain some result of existence and nonexistence of positive weak solution for the following p-Laplacian system $$\begin{equation}\begin{case}-Δ_{pi}u_i=λ_if_i (u_1,…,u_m),\qquad in\;Ω,\;\;i=1,…,m,\\ui=0,\qquad on ∂Ω,\;\;∀i=1,…,m,\end{case}\end{equation}$$ where Δ_{pi}z=div(|∇z|^{pi-2}∇z), pi ≥ 1,λ_i,1 ≤ i ≤ m are a positive parameter, and Ω is a bounded domain in \mathbb{R}^N with smooth boundary ∂Ω. The proof of the main results is based to the method of sub-supersolutions.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v27.n2.6
Journal of Partial Differential Equations, Vol. 27 (2014), Iss. 2 : pp. 158–165
Published online: 2014-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 8
Keywords: Positive solutions