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We compute numerically the minimizers of the Dirichlet energy
among maps 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...
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.
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.
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.
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.
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.
We prove the existence of at least one non-trivial solution for Dirichlet quasilinear elliptic problems. The approach is based on variational methods.
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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