Browsing by Subject "green function"

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Access status: Open Access ,
On the existence of positive continuous solutions for some polyharmonic elliptic systems on the half space
(2012) Zine El Abidine, Zagharide
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 $K^{\infty}_{m,n}(\mathbb{R}^n_+)$.