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  1. Nonlinear Differential Equations and Applications NoDEA
  2. Nonlinear Differential Equations and Applications NoDEA : Volume 18
  3. Nonlinear Differential Equations and Applications NoDEA : Volume 18, Issue 6, December 2011
  4. Changing-sign bubble solutions for an anisotropic sinh-Poisson equation
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Nonlinear Differential Equations and Applications NoDEA : Volume 23
Nonlinear Differential Equations and Applications NoDEA : Volume 22
Nonlinear Differential Equations and Applications NoDEA : Volume 21
Nonlinear Differential Equations and Applications NoDEA : Volume 20
Nonlinear Differential Equations and Applications NoDEA : Volume 19
Nonlinear Differential Equations and Applications NoDEA : Volume 18
Nonlinear Differential Equations and Applications NoDEA : Volume 18, Issue 6, December 2011
Shell model of turbulence perturbed by Lévy noise
Periodic motions in forced problems of Kepler type
General decay of solutions of a nonlinear system of viscoelastic wave equations
Changing-sign bubble solutions for an anisotropic sinh-Poisson equation
On the global well-posedness of a class of Boussinesq–Navier–Stokes systems
Nonlinear Differential Equations and Applications NoDEA : Volume 18, Issue 5, October 2011
Nonlinear Differential Equations and Applications NoDEA : Volume 18, Issue 4, August 2011
Nonlinear Differential Equations and Applications NoDEA : Volume 18, Issue 3, June 2011
Nonlinear Differential Equations and Applications NoDEA : Volume 18, Issue 2, April 2011
Nonlinear Differential Equations and Applications NoDEA : Volume 18, Issue 1, February 2011
Nonlinear Differential Equations and Applications NoDEA : Volume 17
Nonlinear Differential Equations and Applications NoDEA : Volume 16
Nonlinear Differential Equations and Applications NoDEA : Volume 15
Nonlinear Differential Equations and Applications NoDEA : Volume 14
Nonlinear Differential Equations and Applications NoDEA : Volume 13
Nonlinear Differential Equations and Applications NoDEA : Volume 12
Nonlinear Differential Equations and Applications NoDEA : Volume 11
Nonlinear Differential Equations and Applications NoDEA : Volume 10
Nonlinear Differential Equations and Applications NoDEA : Volume 9
Nonlinear Differential Equations and Applications NoDEA : Volume 8
Nonlinear Differential Equations and Applications NoDEA : Volume 7
Nonlinear Differential Equations and Applications NoDEA : Volume 6
Nonlinear Differential Equations and Applications NoDEA : Volume 5
Nonlinear Differential Equations and Applications NoDEA : Volume 4

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Changing-sign bubble solutions for an anisotropic sinh-Poisson equation

Content Provider SpringerLink
Author Wei, Long
Copyright Year 2011
Abstract We consider the following anisotropic sinh-Poisson equation $${\rm div} (a(x) \nabla u)+ 2\varepsilon^2 a(x) {\rm sinh}\,u=0\ \ {\rm in}\ \Omega, \quad u=0 \ \ {\rm on}\ \partial \Omega,$$ where $${\Omega \subset \mathbb{R}^2}$$ is a bounded smooth domain and a(x) is a positive smooth function. We investigate the effect of anisotropic coefficient $${a(x)}$$ on the existence of bubbling solutions. We show that there exists a family of solutions u ε concentrating positively and negatively at $${\bar{x}}$$ , a given local critical point of a(x), for ε sufficiently small, for which with the property $$2\varepsilon^2a(x){\rm sinh} u_\varepsilon \rightharpoonup 8\pi\sum\limits_{j=1}^{m}b_j\delta_{\bar{x}},$$ where $${b_j=\pm 1}$$ . This result shows a striking difference with the isotropic case (a(x) ≡ Constant) in Bartolucci and Pistoia (IMA J Appl Math 72(6):706–729, 2007), Jost et al. (Calc Var Partial Differ Equ 31:263–276, 2008) and Esposito and Wei (Calc Var Partial Differ Equ 34:341–375, 2009).
Ending Page 706
Page Count 22
Starting Page 685
File Format PDF
ISSN 10219722
e-ISSN 14209004
Journal Nonlinear Differential Equations and Applications NoDEA
Issue Number 6
Volume Number 18
Language English
Publisher SP Birkhäuser Verlag Basel
Publisher Date 2011-08-04
Publisher Place Basel
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Analysis Non-simple blow-up solutions sinh-Poisson equation Variational methods for second-order elliptic equations Nonlinear boundary value problems for linear elliptic equations
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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