Lane-Emden System

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

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

$$J(u,v)={\int }_{\mathrm{\Omega }}\nabla u\nabla vdx-{\int }_{\mathrm{\Omega }}(\frac{1}{q+1}{u}^{q+1}+\frac{1}{p+1}{v}^{p+1})𝑑x.$$

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