TY  - JOUR
ID  - ElAbidine2012
LB  - ElAbidine2012
AU  - El Abidine, Zagharide Zine
TI  - On the existence of positive continuous solutions for some polyharmonic elliptic systems on the half space
ST  - On the existence of positive continuous solutions for some polyharmonic elliptic systems on the half space
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2012
VL  - 32
IS  - 1
SP  - 91
EP  - 113
DO  - http://dx.doi.org/10.7494/OpMath.2012.32.1.91
UR  - http://dx.doi.org/10.7494/OpMath.2012.32.1.91
AB  - 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 \(K^{\infty}_{m,n}(\mathbb{R}^n_+)\).
KW  - polyharmonic elliptic system
KW  - Green function
KW  - Kato class
KW  - positive continuous solution
KW  - Schauder fixed point theorem
SN  - 1232-9274
ER  -