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IMA Journal of Applied Mathematics Advance Access originally published online on August 16, 2007
IMA Journal of Applied Mathematics 2007 72(6):706-729; doi:10.1093/imamat/hxm012
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© The Author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Existence and qualitative properties of concentrating solutions for the sinh-Poisson equation

Daniele Bartolucci{dagger}

Dipartimento di Matematica "L.Castelnuovo," Università di Roma "Tor Vergata," Via della Ricerca Scientifica, 00133 Roma, Italy

Angela Pistoia{ddagger}

Dipartimento di Metodi e Modelli Matematici, Università di Roma "La Sapienza," Via Scarpa 16, 00166 Roma, Italy

{dagger} Email: bartoluc{at}mat.uniroma1.it

{ddagger} Email: pistoia{at}dmmm.uniroma1.it

Received on June 9, 2006; Revision received October 29, 2006. Accepted on November 21, 2006

We prove the existence of nodal solutions for – {Delta}u = {rho} sinh u with Dirichlet boundary conditions in bounded, 2D, smooth and non-smooth domains. Indeed, for {rho} positive and small enough, we show that there exist at least two pairs of solutions, which change sign exactly once, whose nodal lines intersect the boundary.

Keywords: nodal solutions; nodal lines; vortices.


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