Lane-Emden System

Lane-Emden System Here is an example of Hamiltonian elliptic systems, also called the Lane-Emden system,

(LE)\;\left\{\begin{array}[]{ll}-\Delta u=v^{p}&\,x\in\Omega,\\ -\Delta v=u^{q}&\,x\in\Omega,\\ u=v=0&\,x\in\partial\Omega,\end{array}\right.

where $p,q>0,\Omega\subset{\mathbb{R}}^{N}(N\geq 1)$ is an open bounded domain. (LE) is called sublinear (superlinear) if $pq<1\;(pq>1)$ . The associated energy functional to (LE) is

J(u,v)=\int_{\Omega}\nabla u\nabla vdx-\int_{\Omega}(\frac{1}{q+1}u^{q+1}+% \frac{1}{p+1}v^{p+1})dx.

Title	Lane-Emden System
Canonical name	LaneEmdenSystem
Date of creation	2013-03-11 19:34:47
Last modified on	2013-03-11 19:34:47
Owner	linor (11198)
Last modified by	(0)
Numerical id	1
Author	linor (0)
Entry type	Definition