@Article{ElAbidine2012,
author = "El Abidine, Zagharide Zine",
title = "On the existence of positive continuous solutions for some polyharmonic elliptic systems on the half space",
journal = "Opuscula Math.",
year = "2012",
volume = "32",
number = "1",
pages = "91--113",
doi = "http://dx.doi.org/10.7494/OpMath.2012.32.1.91",
url = "http://dx.doi.org/10.7494/OpMath.2012.32.1.91",
abstract = "We study the existence of positive continuous solutions of the nonlinear polyharmonic system \((-\Delta)^m u + \lambda q g(v) = 0\); \((-\Delta)^m v + \mu p f(u) = 0\) in the half space \(\mathbb{R}^n_+:=\{x = (x_1,...,x_n) \in \mathbb{R}^n : x_n \gt 0\}\), where \(m \geq 1\) and \(n \gt 2m\). The nonlinear term is required to satisfy some conditions related to the Kato class \(K^{\infty}_{m,n}(\mathbb{R}^n_+)\). Our arguments are based on potential theory tools associated to \((-\Delta)^m\) and properties of functions belonging to \(K^{\infty}_{m,n}(\mathbb{R}^n_+)\).",
keywords = "polyharmonic elliptic system, Green function, Kato class, positive continuous solution, Schauder fixed point theorem",
issn = "1232-9274"
}