Hamiltonian-type elliptic system

A Hamiltonian elliptic system is of the form

\begin{displaymath} (HS) \;\; \left \{ \begin{array}{ll} -\Delta u= G_v(x; u,v... ...{\partial n}=0 &\, x\in \partial \Omega \end{array} \right. \end{displaymath}

where $\Omega\subset {\mathbb{R}}^N (N\ge 1)$ is an open bounded domain, $G(x; u,v)\in \mathcal{C}^{1}(\overline{\Omega} \times \mathbb{R}^2; \mathbb{R})$ in the variables $(u,v) \in \mathbb{R}^2$ with $\nabla G =(G_u, G_v)$.

Particular examples of Hamiltonian elliptic systems include the Lane-Emden system and semilinear biharmonic problems.



Created by Xianjin Chen

Nov-30-2007