## Advances in Differential Equations

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

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

#### Abstract

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

**Source**

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

**Dates**

First available in Project Euclid: 2 January 2013

**Permanent link to this document**

https://projecteuclid.org/euclid.ade/1357141854

**Mathematical Reviews number (MathSciNet)**

MR1826720

**Zentralblatt MATH identifier**

1142.35345

**Subjects**

Primary: 35B40: Asymptotic behavior of solutions

Secondary: 35J50: Variational methods for elliptic systems 35J60: Nonlinear elliptic equations

#### Citation

Isobe, Takeshi. On the asymptotic analysis of $H$-systems. I. Asymptotic behavior of large solutions. Adv. Differential Equations 6 (2001), no. 5, 513--546. https://projecteuclid.org/euclid.ade/1357141854