## Differential and Integral Equations

### Classification of blow-up limits for the sinh-Gordon equation

#### Abstract

The aim of this paper is to use a selection process and a careful study of the interaction of bubbling solutions to show a classification result for the blow-up values of the elliptic sinh-Gordon equation $$\Delta u+h_1e^u-h_2e^{-u}=0 \qquad \mathrm{in}~B_1\subset\mathbb R^2.$$ In particular, we get that the blow-up values are multiple of $8\pi.$ It generalizes the result of Jost, Wang, Ye and Zhou [20] where the extra assumption $h_1 = h_2$ is crucially used.

#### Article information

Source
Differential Integral Equations, Volume 31, Number 9/10 (2018), 657-684.

Dates
First available in Project Euclid: 13 June 2018