TY - JOUR
T1 - Existence and Nonexistence of Weak Positive Solution for a Class of <em>p</em>-Laplacian Systems
AU - Akrout , Kamel
AU - Guefaifia , Rafik
JO - Journal of Partial Differential Equations
VL - 2
SP - 158
EP - 165
PY - 2014
DA - 2014/06
SN - 27
DO - http://doi.org/10.4208/jpde.v27.n2.6
UR - https://global-sci.org/intro/article_detail/jpde/5133.html
KW - Positive solutions
KW - sub-supersolutions
KW - elliptic systems
AB - 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.