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Uniqueness of solutions and linearized stability for impulsive differential equations with state-dependent delay.
- Source :
-
Journal of Differential Equations . Nov2022, Vol. 338, p415-440. 26p. - Publication Year :
- 2022
-
Abstract
- We prove that under fairly natural conditions on the state space and nonlinearities, it is typical for an impulsive differential equation with state-dependent delay to exhibit non-uniqueness of solutions. On a constructive note, we show that uniqueness of solutions can be recovered using a Winston-type condition on the state-dependent delay. Irrespective of uniqueness of solutions, we prove a result on linearized stability. As a specific application, we consider a scalar equation on the positive half-line with continuous-time negative feedback, non-negative state-dependent delayed nonlinearity and impulse effect functional satisfying affine bounds. [ABSTRACT FROM AUTHOR]
- Subjects :
- *IMPULSIVE differential equations
*DELAY differential equations
Subjects
Details
- Language :
- English
- ISSN :
- 00220396
- Volume :
- 338
- Database :
- Academic Search Index
- Journal :
- Journal of Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 159328882
- Full Text :
- https://doi.org/10.1016/j.jde.2022.08.009