论文标题
liouville类型的结果和对系统的量化效果$-ΔU= u J'（1- | u |^{2}）$，用于零接近零的电位凸
A Liouville type result and quantization effects on the system $-Δu = u J'(1-|u|^{2})$ for a potential convex near zero
论文作者
论文摘要
我们考虑$-ΔU= u J'（1- | U |^{2}）$的$ \ r^2 $中的Ginzburg-landau类型方程，具有潜在函数$ J $满足弱条件的潜在函数$ J $，例如，允许较弱的条件允许在原点中的无限顺序零。在这种情况下，我们扩展了有关H.Brezis，F.Merle，T.Rivière的有限潜在解决方案的结果，这些结果是\ cite {bmr}的，当$ j $在$ j $的情况下对情况进行治疗时，以及TH的结果。 Cazenave，在相同的参考文献中发现，以及有限能量解决方案的形式。
We consider a Ginzburg-Landau type equation in $\R^2$ of the form $-Δu = u J'(1-|u|^{2})$ with a potential function $J$ satisfying weak conditions allowing for example a zero of infinite order in the origin. We extend in this context the results concerning quantization of finite potential solutions of H.Brezis, F.Merle, T.Rivière from \cite{BMR} who treat the case when $J$ behaves polinomially near 0, as well as a result of Th. Cazenave, found in the same reference, and concerning the form of finite energy solutions.
