Abstract
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.
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Tudoran, R.M. On the Coercivity of Continuously Differentiable Vector Fields. Qual. Theory Dyn. Syst. 19, 58 (2020). https://doi.org/10.1007/s12346-020-00394-1
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DOI: https://doi.org/10.1007/s12346-020-00394-1