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Newton and conjugate gradient for harmonic maps from the disc into the sphere

Morgan Pierre (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We compute numerically the minimizers of the Dirichlet energy E ( u ) = 1 2 ∫ B 2 | ∇ u | 2 d x among maps u : B 2 → S 2 from the unit disc into the unit sphere that satisfy a boundary condition and a degree condition. We use a Sobolev gradient algorithm for the minimization and we prove that its continuous version preserves the degree. For the discretization of the problem we use continuous P1 finite elements. We propose an original mesh-refining strategy needed to preserve the degree with the discrete version of the algorithm (which...

Nonlinear Variational Inequalities Depending on a Parameter

Goeleven, D., Théra, M. (1995)

Serdica Mathematical Journal

This paper develops the results announced in the Note [14]. Using an eigenvalue problem governed by a variational inequality, we try to unify the theory concerning the post-critical equilibrium state of a thin elastic plate subjected to unilateral conditions.

Nonlinear vibrations of completely resonant wave equations

Massimiliano Berti (2007)

Banach Center Publications

We present recent existence results of small amplitude periodic and quasi-periodic solutions of completely resonant nonlinear wave equations. Both infinite-dimensional bifurcation phenomena and small divisors difficulties occur. The proofs rely on bifurcation theory, Nash-Moser implicit function theorems, dynamical systems techniques and variational methods.

Non-topological condensates in self-dual Chern-Simons gauge theory

Takashi Suzuki, Futoshi Takahashi (2004)

Banach Center Publications

This note is concerned with the recent paper "Non-topological N-vortex condensates for the self-dual Chern-Simons theory" by M. Nolasco. Modifying her arguments and statements, we show that the existence of "non-topological" multi-vortex condensates follows when the number of prescribed vortex points is greater than or equal to 2.

Nontrivial critical points of asymptotically quadratic functions at resonances

Michal Fečkan (1997)

Annales Polonici Mathematici

Asymptotically quadratic functions defined on Hilbert spaces are studied by using some results of the theory of Morse-Conley index. Applications are given to existence of nontrivial weak solutions for asymptotically linear elliptic partial and ordinary differential equations at resonances.

Nontrivial examples of coupled equations for Kähler metrics and Yang-Mills connections

Julien Keller, Christina Tønnesen-Friedman (2012)

Open Mathematics

We provide nontrivial examples of solutions to the system of coupled equations introduced by M. García-Fernández for the uniformization problem of a triple (M; L; E), where E is a holomorphic vector bundle over a polarized complex manifold (M, L), generalizing the notions of both constant scalar curvature Kähler metric and Hermitian-Einstein metric.

Nontrivial Solutions of Quasilinear Equations In BV

Marzocchi, Marco (1996)

Serdica Mathematical Journal

The existence of a nontrivial critical point is proved for a functional containing an area-type term. Techniques of nonsmooth critical point theory are applied.

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