On Differential Equations with Codimension-$n$ Discontinuity Sets

2021 ◽  
Vol 20 (3) ◽  
pp. 1348-1381
Author(s):  
Peter L. Varkonyi ◽  
Mate Antali
Keyword(s):  
Differential Equations ◽  
Discontinuity Sets

Ordinary differential equations and systems with time-dependent discontinuity sets

2004 ◽  
Vol 134 (4) ◽  
pp. 617-637 ◽  
Author(s):  
J. Ángel Cid ◽  
Rodrigo L. Pouso
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Autonomous Systems ◽  
Existence Results ◽  
Time Dependent ◽  
Nonlinear Part ◽  
First Order ◽  
Discontinuity Sets

In this paper we prove new existence results for non-autonomous systems of first order ordinary differential equations under weak conditions on the nonlinear part. Discontinuities with respect to the unknown are allowed to occur over general classes of time-dependent sets which are assumed to satisfy a kind of inverse viability condition.

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