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

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

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

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Veröffentlicht in:IMA journal of applied mathematics 2007-12, Vol.72 (6), p.706-729
Hauptverfasser: Bartolucci, Daniele, Pistoia, Angela
Format: Artikel
Sprache:eng
Schlagworte:
Exact sciences and technology
Mathematical analysis
Mathematics
nodal lines
nodal solutions
Partial differential equations
Sciences and techniques of general use
vortices
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Zusammenfassung:We prove the existence of nodal solutions for – Δu = ρ sinh u with Dirichlet boundary conditions in bounded, 2D, smooth and non-smooth domains. Indeed, for ρ 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.
ISSN:0272-4960
1464-3634
DOI:10.1093/imamat/hxm012