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On the Coercivity of Continuously Differentiable Vector Fields
Qualitative Theory of Dynamical Systems ( IF 1.4 ) Pub Date : 2020-04-13 , DOI: 10.1007/s12346-020-00394-1
Răzvan M. Tudoran

Given an arbitrary fixed continuously differentiable vector field on \(\mathbb {R}^n\), we prove that this vector field is coercive if and only if its conservative part is coercive. We apply this result in order to provide sufficient conditions to guarantee the co-existence of equilibrium states of a continuously differentiable vector field and its conservative part.

中文翻译:

关于连续可微向量场的矫顽力

给定\(\ mathbb {R} ^ n \)上的任意固定的连续可微向量场,我们证明了当且仅当它的保守部分是强制性时,此向量域才是强制性的。我们应用此结果是为了提供足够的条件,以保证连续可微向量场及其保守部分的平衡状态并存。
更新日期:2020-04-13
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