Approximate and Near Weak Invariance for Nonautonomous Differential Inclusions

作者：Benniche Omar; Carja Ovidiu^*

来源：Journal of Dynamical and Control Systems, 2017, 23(2): 249-268.

DOI：10.1007/s10883-016-9312-0

• Approximate/near weak invariance
• Tangency conditions
• Differential inclusions

Let X be a real Banach space and I a nonempty interval. Let K : I (sic) X be a multi-function with the graph K. We give here a characterization for K to be approximate/near weakly invariant with respect to the differential inclusion x' (t) F(t, x(t)) by means of an appropriate tangency concept and Lipschitz conditions on F. The tangency concept introduced in this paper extends in a natural way the quasi-tangency concept introduced by Carja et al. (Trans Amer Math Soc. 2009; 361: 343-90) (see also Carja et al. (2007)). Viability, invariance and applications. Amsterdam: Elsevier Science B V) in the case when F is independent of t. As an application, we give some results concerning the set of solutions for the differential inclusion x' (t) F(t, x(t)).

• 出版日期2017-4