@Article{Turki2012,
author = "Turki, Sameh",
title = "Existence and asymptotic behavior of positive continuous solutions for a nonlinear elliptic system in the half space",
journal = "Opuscula Math.",
year = "2012",
volume = "32",
number = "4",
pages = "783--795",
doi = "http://dx.doi.org/10.7494/OpMath.2012.32.4.783",
url = "http://dx.doi.org/10.7494/OpMath.2012.32.4.783",
abstract = "This paper deals with the existence and the asymptotic behavior of positive continuous solutions of the nonlinear elliptic system \(\Delta u=p(x)u^{\alpha}v^r\), \(\Delta v = q(x)u^s v^{\beta}\), in the half space \(\mathbb{R}^n_+ :=\{x=(x_1,..., x_n)\in \mathbb{R}^n : x_n \gt 0\}\), \(n \geq 2\), where \(\alpha, \beta \gt 1\) and \(r, s \geq 0\). The functions \(p\) and \(q\) are required to satisfy some appropriate conditions related to the Kato class \(K^{\infty}(\mathbb{R}^n_+)\). Our approach is based on potential theory tools and the use of Schauder's fixed point theorem.",
keywords = "asymptotic behavior, elliptic system, regular equation",
issn = "1232-9274"
}