TY  - JOUR
ID  - Turki2012
LB  - Turki2012
AU  - Turki, Sameh
TI  - Existence and asymptotic behavior of positive continuous solutions for a nonlinear elliptic system in the half space
ST  - Existence and asymptotic behavior of positive continuous solutions for a nonlinear elliptic system in the half space
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2012
VL  - 32
IS  - 4
SP  - 783
EP  - 795
DO  - http://dx.doi.org/10.7494/OpMath.2012.32.4.783
UR  - http://dx.doi.org/10.7494/OpMath.2012.32.4.783
AB  - 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.
KW  - asymptotic behavior
KW  - elliptic system
KW  - regular equation
SN  - 1232-9274
ER  -