Advances in Differential Equations

On the asymptotic analysis of $H$-systems. I. Asymptotic behavior of large solutions

Takeshi Isobe

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


Let $\Omega\subset\mathbb R^2$ be a bounded domain, $\gamma\in C^{3,\alpha}(\partial\Omega;\mathbb R^3 )$ $(0 <\alpha <1)$ and $H>0$. We consider the asymptotic behavior of large solutions of an $H$-system $$\Delta u=2Hu_{x_1}\wedge u_{x_2}\quad\text{in $\Omega$}, \qquad u=\gamma\quad \text{on $\partial\Omega$}$$ as $H\to 0$ or as $\gamma\to 0$. We show that large solutions blow up at exactly one point in $\Omega$. The exact blow-up rate and location of blow-up point are studied.

Article information

Adv. Differential Equations Volume 6, Number 5 (2001), 513-546.

First available in Project Euclid: 2 January 2013

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35B40: Asymptotic behavior of solutions
Secondary: 35J50: Variational methods for elliptic systems 35J60: Nonlinear elliptic equations


Isobe, Takeshi. On the asymptotic analysis of $H$-systems. I. Asymptotic behavior of large solutions. Adv. Differential Equations 6 (2001), no. 5, 513--546.

Export citation