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.
Let X be a finite CW complex, and ρ: π 1(X) → GL(l, ℂ) a representation. Any cohomology class α ∈ H 1(X, ℂ) gives rise to a deformation γ t of ρ defined by γ t (g) = ρ(g) exp(t〈α, g〉). We show that the cohomology of X with local coefficients γ gen corresponding to the generic point of the curve γ is computable from a spectral sequence starting from H*(X, ρ). We compute the differentials of the spectral sequence in terms of the Massey products and show that the spectral sequence degenerates in case...