Abstract
We consider the sinh-Poisson equation
, where Ω is a smooth bounded domain in \({\mathbb{R}^2}\) and λ is a small positive parameter. If \({0 \in \Omega}\) and Ω is symmetric with respect to the origin, for any integer k if λ is small enough, we construct a family of solutions to (P) λ , which blows up at the origin, whose positive mass is 4πk(k−1) and negative mass is 4πk(k + 1). This gives a complete answer to an open problem formulated by Jost et al. (Calc Var PDE 31(2):263–276, 2008).
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Grossi, M., Pistoia, A. Multiple Blow-Up Phenomena for the Sinh-Poisson Equation. Arch Rational Mech Anal 209, 287–320 (2013). https://doi.org/10.1007/s00205-013-0625-9
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DOI: https://doi.org/10.1007/s00205-013-0625-9