一类Ginzburg-Landau型泛函的径向极小元的渐近性

The behavior of radial minimizers for a Ginzburg-Landau type functional is considered. The weak convergence of minimizers in W1,n is improved to the strong convergence in W1,n. Some estimates of the rate of the convergence for the module of minimizers are presented.     

含有杂质的Ginzburg-Landau泛函的径向极小元

研究了含有杂质的超导体的Ginzburg—Landau模型，给出了Ginzburg—Landau泛函的径向极小元的零点分布，并证明了径向极小元的惟一性。     

关于一类Ginzburg-Landau型泛函径向极小元的注记

考虑的是Bethuel，Brczis和Helcin在[1]中提出的问题7．针对Ginzburg-Landau泛函的径向极小元，作者给出了这一问题的肯定回答．     

p-Ginzburg-Landau型极小元的渐近性质与p-调和映射的关系

本文考虑的是一类p-Ginzburg-Landau型泛函极小元,当p∈(1,n)时的极限行为.研究了极小元的零点与p-调和映射的奇点间的关系,并证明了极小元在C1,γloc意义下收敛到p-调和映射.     

p-Ginzburg-Landau型极小元的渐近性质与p-调和映射的关系

本文考虑的是一类p-Ginzburg-Landau型泛函极小元,当p∈(1,n)时的极限行为．研究了极小元的零点与p-调和映射的奇点间的关系,并证明了极小元在Cloc1,γ意义下收敛到p-调和映射．     

一类Euler方程解的渐近行为

给出了一类Ginzburg-Landau型泛函的极小元所满足的Euler方程的解的某些弱收敛性质。     

一类不可微泛函拟极小问题的C1,α正则性

考虑一类不可微泛函I(u,G) =∫GF(x,u, u)dx的拟极小问题,证明了解的局部C1,α正则性,推广和发展了Anzellotti[6]的一些成果,而且与Anzellotti的方法不同.     

一类高维滞后型泛函微分方程的周期解

本文研究一类滞后型函数分方程的周期解问题，利用指数型二分性和不动点定理，在较广泛的条件下证明了该方程的周期解的存在性及唯一性，推广并改进了文[1-3]的主要结果     

一类二阶中立型偏泛函微分方程的振动性

获得了一类具连续偏差变元二阶非线性中立型偏微分方程的振动性的充分性条件.     

带积分限制的二次泛函极小的正则性

本文用直接方法证明了二次泛函在集合中的极小u,当n=2时,且,其中q>2,0<α<1     

Uniqueness Theorem of the Regularizable Redial Ginzburg-Landau Type Minimizers

The author proves the uniqueness of the regularizable radial minimizers of a Ginzburg-Landau type functional in the case n - 1 < p < n,and the location of the zeros of the regularizable radial minimizers of this functional is discussed.     

Local minimizers of the Ginzburg-Landau functional with prescribed degrees

We consider, in a smooth bounded multiply connected domain D⊂R², the Ginzburg-Landau energy subject to prescribed degree conditions on each component of ∂D. In general, minimal energy maps do not exist [L. Berlyand, P. Mironescu, Ginzburg-Landau minimizers in perforated domains with prescribed degrees, preprint, 2004]. When D has a single hole, Berlyand and Rybalko [L. Berlyand, V. Rybalko, Solution with vortices of a semi-stiff boundary value problem for the Ginzburg-Landau equation, J. Eur. Math. Soc. (JEMS), in press, 2008, http://www.math.psu.edu/berlyand/publications/publications.html] proved that for small ε local minimizers do exist. We extend the result in [L. Berlyand, V. Rybalko, Solution with vortices of a semi-stiff boundary value problem for the Ginzburg-Landau equation, J. Eur. Math. Soc. (JEMS), in press, 2008, http://www.math.psu.edu/berlyand/publications/publications.html]: Eε(u) has, in domains D with 2,3,… holes and for small ε, local minimizers. Our approach is very similar to the one in [L. Berlyand, V. Rybalko, Solution with vortices of a semi-stiff boundary value problem for the Ginzburg-Landau equation, J. Eur. Math. Soc. (JEMS), in press, 2008, http://www.math.psu.edu/berlyand/publications/publications.html]; the main difference stems in the construction of test functions with energy control.     

Asymptotic analysis for the radial minimizer of a second-order energy functional

The convergence for the radial minimizers of a second-order energy functional, when the parameter tends to 0 is studied. And the location of the zeros of the radial minimizers of this functional is presented. Based on this result, the uniqueness of the radial minimizer is discussed.     

PINNING OF VORTICES FOR THE GINZBURG-LANDAU FUNCTIONAL WITH VARIABLE COEFFICIENT

In this paper, the asymptotic behavior as ε→O of the minimizers u,of the Ginzburg Lan-dau functional with variable coefficient is discussed. The singularities are found to be located at thepoints which globally minimize the coefficient. The zeros of u, are accumulated near the singulari-ties as is small enough. This verifies the pinning mechanism.     

Quantization for a Ginzburg-Landau type energy related to superconductivity with normal impurity inclusion

The author applies Pohozaev identity to research the quantization for a Ginzburg-Landau type functional related to superconductivity with normal impurity inclusion. Under the different assumptions, the author obtains the quantization results by dealing with the defect on the junction.     

Local minimizers with vortex pinning to Ginzburg-Landau functional in three dimensions

We consider the pinning effect for full Ginzburg-Landau functional. The existence of local minimizers with vortices locating in the pinning regions is obtained.