An exact multiplicity result for a class of symmetric problems

2008 ◽  
pp. 257-260
Author(s):  
Philip Korman
Keyword(s):  
Multiplicity Result ◽  
Exact Multiplicity

Vortex structures for an SO(5) model of high-TC superconductivity and antiferromagnetism

2000 ◽  
Vol 130 (6) ◽  
pp. 1183-1215 ◽  
Author(s):  
S. Alama ◽  
L. Bronsard ◽  
T. Giorgi
Keyword(s):  
Chemical Potential ◽  
High Temperature Superconductivity ◽  
Landau Theory ◽  
Threshold Level ◽  
Simple Eigenvalue ◽  
Core Region ◽  
Multiplicity Result ◽  
Ginzburg Landau ◽  
Antiferromagnetic Ordering ◽  
Exact Multiplicity

We study the structure of symmetric vortices in a Ginzburg–Landau model based on Zhang's SO(5) theory of high-temperature superconductivity and antiferromagnetism. We consider both a full Ginzburg–Landau theory (with Ginzburg–Landau scaling parameter κ < ∞) and a κ → ∞ limiting model. In all cases we find that the usual superconducting vortices (with normal phase in the central core region) become unstable (not energy minimizing) when the chemical potential crosses a threshold level, giving rise to a new vortex profile with antiferromagnetic ordering in the core region. We show that this phase transition in the cores is due to a bifurcation from a simple eigenvalue of the linearized equations. In the limiting large-κ model, we prove that the antiferromagnetic core solutions are always non-degenerate local energy minimizers and prove an exact multiplicity result for physically relevant solutions.

scholarly journals A MULTIPLICITY RESULT FOR A CLASS OF EQUATIONS OFp-LAPLACIAN TYPE WITH SIGN-CHANGING NONLINEARITIES

2009 ◽  
Vol 51 (3) ◽  
pp. 513-524 ◽  
Author(s):  
NGUYEN THANH CHUNG ◽  
QUỐC ANH NGÔ
Keyword(s):  
Bounded Domain ◽  
Multiplicity Result ◽  
Positive Parameter ◽  
Existence And Multiplicity ◽  
Carathéodory Function ◽  
Image Position

AbstractUsing variational arguments we study the non-existence and multiplicity of non-negative solutions for a class equations of the formwhere Ω is a bounded domain inN,N≧ 3,fis a sign-changing Carathéodory function on Ω × [0, +∞) and λ is a positive parameter.

scholarly journals On the Existence of Nodal Solutions for a Nonlinear Elliptic Problem on Symmetric Riemannian Manifolds

2010 ◽  
Vol 2010 ◽  
pp. 1-11 ◽  
Author(s):  
Anna Maria Micheletti ◽  
Angela Pistoia
Keyword(s):  
Riemannian Manifold ◽  
Riemannian Manifolds ◽  
Elliptic Problem ◽  
Multiplicity Result ◽  
Nonlinear Elliptic Problem ◽  
Nodal Solutions ◽  
Nonlinear Elliptic ◽  
Sign Changing Solutions

Given thatis a smooth compact and symmetric Riemannian -manifold, , we prove a multiplicity result for antisymmetric sign changing solutions of the problem in . Here if and if .

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