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Periodic Solutions in Slowly Varying Discontinuous Differential Equations: A Non-Generic Case.
- Source :
-
Journal of Dynamics & Differential Equations . Mar2024, Vol. 36 Issue 1, p463-496. 34p. - Publication Year :
- 2024
-
Abstract
- We derive Melnikov type conditions for the persistence of periodic solutions in perturbed slowly varying discontinuous differential equations. In contrast to Battelli and Fečkan (Mathematics 9(19):2449, 2021) we assume that the unperturbed (frozen) equation has a family of periodic solutions depending on some parameters. The result of this paper are motivated by and extend a result in Wiggins and Holmes (SIAM J Math Anal 18:592–611, 1987) where the authors considered a two dimensional hamiltonian family of smooth systems depending on a scalar variable which is the solution of a singularly perturbed equation. [ABSTRACT FROM AUTHOR]
- Subjects :
- *DIFFERENTIAL equations
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 10407294
- Volume :
- 36
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Dynamics & Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 175720190
- Full Text :
- https://doi.org/10.1007/s10884-022-10155-0