We consider the sinh-Poisson equation (P)λ - Δu = λ sinh u in Ω, u=0 on ∂Ω, where Ω is a smooth bounded domain in ℝ2 and λ is a small positive parameter. If 0 ∈ Ω 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). © 2013 Springer-Verlag Berlin Heidelberg.
Multiple Blow-Up Phenomena for the Sinh-Poisson Equation / Grossi, Massimo; Pistoia, Angela. - In: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS. - ISSN 0003-9527. - 209:1(2013), pp. 287-320. [10.1007/s00205-013-0625-9]
Multiple Blow-Up Phenomena for the Sinh-Poisson Equation
GROSSI, Massimo;PISTOIA, Angela
2013
Abstract
We consider the sinh-Poisson equation (P)λ - Δu = λ sinh u in Ω, u=0 on ∂Ω, where Ω is a smooth bounded domain in ℝ2 and λ is a small positive parameter. If 0 ∈ Ω 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). © 2013 Springer-Verlag Berlin Heidelberg.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
