Advances in Differential Equations

Nodal bubbling solutions to a weighted sinh-Poisson equation

Yang Wang and Long Wei

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


We consider the existence of multiple nodal bubbling solutions to the equation $-{\Delta } u=2\ {\varepsilon }^2|x|^{2\alpha}\sinh u$ posed on a bounded smooth domain ${\Omega }$ in $\mathbb{R}^2$ with homogeneous Dirichlet boundary conditions. By construction, we show that there exists a solution such that $2{\varepsilon }^2|x|^{2\alpha}\sinh u_{{\varepsilon }}$ develops not only many positive and negative Dirac deltas with weights $8\pi$ and $-8\pi$ respectively, but also a Dirac delta with weight $8\pi(1+\alpha)$ at the origin, where $\alpha\not\in \mathbb{N}$. In particular, we provide explicit examples to show the existence of nodal bubbling solutions to our problem in the unit disc in $\mathbb R^2$.

Article information

Adv. Differential Equations Volume 13, Number 9-10 (2008), 881-906.

First available in Project Euclid: 18 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J60: Nonlinear elliptic equations
Secondary: 35J20: Variational methods for second-order elliptic equations 35J25: Boundary value problems for second-order elliptic equations


Wang, Yang; Wei, Long. Nodal bubbling solutions to a weighted sinh-Poisson equation. Adv. Differential Equations 13 (2008), no. 9-10, 881--906.

Export citation