[BOOK][B] The Mountain Pass Theorem: variants, generalizations and some applications
Y Jabri - 2003 - books.google.com
This 2003 book presents min-max methods through a study of the different faces of the
celebrated Mountain Pass Theorem (MPT) of Ambrosetti and Rabinowitz. The reader is led …
celebrated Mountain Pass Theorem (MPT) of Ambrosetti and Rabinowitz. The reader is led …
Stability of point defects of degree in a two-dimensional nematic liquid crystal model
We study k-radially symmetric solutions corresponding to topological defects of charge k 2 k
2 for integer k\not= 0 k≠ 0 in the Landau-de Gennes model describing liquid crystals in two …
2 for integer k\not= 0 k≠ 0 in the Landau-de Gennes model describing liquid crystals in two …
Local minimality of RN-valued and SN-valued Ginzburg–Landau vortex solutions in the unit ball BN
R Ignat, L Nguyen - arxiv preprint arxiv:2111.07669, 2021 - ems.press
Local minimality of RN -valued and SN -valued Ginzburg–Landau vortex solutions in the unit
ball BN Page 1 Ann. Inst. H. PoincarÈ Anal. Non LinÈaire (Online first) DOI 10.4171/AIHPC/84 …
ball BN Page 1 Ann. Inst. H. PoincarÈ Anal. Non LinÈaire (Online first) DOI 10.4171/AIHPC/84 …
Dynamic stability of magnetic vortices
S Gustafson - Nonlinearity, 2002 - iopscience.iop.org
The well-known equivariant (radially-symmetric) vortex solutions of the Ginzburg–Landau
equations of superconductivity are static solutions of several time-dependent equations. We …
equations of superconductivity are static solutions of several time-dependent equations. We …
On the structure of fractional degree vortices in a spinor Ginzburg–Landau model
We consider a Ginzburg–Landau functional for a complex vector order parameter Ψ=(ψ+,
ψ−), whose minimizers exhibit vortices with half-integer degree. By studying the associated …
ψ−), whose minimizers exhibit vortices with half-integer degree. By studying the associated …
A symmetry breaking phenomenon for anisotropic harmonic maps from a 2D annulus into
A Contreras, X Lamy - arxiv preprint arxiv:2311.15758, 2023 - arxiv.org
In a two dimensional annulus $ A_\rho=\{x\in\mathbb R^ 2:\rho<| x|< 1\} $, $\rho\in (0, 1) $,
we characterize $0 $-homogeneous minimizers, in $ H^ 1 (A_\rho;\mathbb S^ 1) $ with …
we characterize $0 $-homogeneous minimizers, in $ H^ 1 (A_\rho;\mathbb S^ 1) $ with …
[HTML][HTML] Symmetric vortices for two-component Ginzburg–Landau systems
S Alama, Q Gao - Journal of Differential Equations, 2013 - Elsevier
Abstract We study Ginzburg–Landau equations for a complex vector order parameter
Ψ=(ψ+, ψ−)∈ C 2. We consider symmetric vortex solutions in the plane R 2, ψ (x)= f±(r) …
Ψ=(ψ+, ψ−)∈ C 2. We consider symmetric vortex solutions in the plane R 2, ψ (x)= f±(r) …
On the symmetry and uniqueness of solutions of the Ginzburg–Landau equations for small domains
A Aftalion, EN Dancer - Communications in Contemporary …, 2001 - World Scientific
In this paper, we study the Ginzburg–Landau equations for a two dimensional domain which
has small size. We prove that if the domain is small, then the solution has no zero, that is no …
has small size. We prove that if the domain is small, then the solution has no zero, that is no …
Infinitely many multi-vortex solutions of the magnetic Ginzburg–Landau equation with external potentials in R2
J Wei, Y Wu - Journal of Mathematical Physics, 2021 - pubs.aip.org
In this paper, we consider the magnetic Ginzburg–Landau equation with external potentials
μV (x) for the type II superconductors. We prove, by reduction arguments, that under suitable …
μV (x) for the type II superconductors. We prove, by reduction arguments, that under suitable …
Fourfold symmetric solutions to the Ginzburg Landau equation for d-wave superconductors
M Kim, D Phillips - Communications in Mathematical Physics, 2012 - Springer
We find and investigate the structure of solutions to the Ginzburg Landau equation for a high
temperature superconductor with tetragonal symmetry. This is done near an isolated …
temperature superconductor with tetragonal symmetry. This is done near an isolated …