6533b85ffe1ef96bd12c101f
RESEARCH PRODUCT
Periodic solutions of a class of non-autonomous second order differential equations with discontinuous right-hand side
Alain JacquemardMarco Antonio Teixeirasubject
Class (set theory)Second order differential equationsWork (thermodynamics)SingularityDynamical systems theoryDifferential equationMathematical analysisSecond order equationStatistical and Nonlinear PhysicsCondensed Matter PhysicsMathematicsdescription
Abstract The main goal of this paper is to discuss the existence of periodic solutions of the second order equation: y ″ + η sgn ( y ) = α sin ( β t ) with ( η , α , β ) ∈ R 3 η > 0 . We analyze the dynamics of such an equation around the origin which is a typical singularity of non-smooth dynamical systems. The main results consist in exhibiting conditions on the existence of typical periodic solutions that appear generically in such systems. We emphasize that the mechanism employed here is applicable to many more systems. In fact this work fits into a general program for understanding the dynamics of non-autonomous differential equations with discontinuous right-hand sides.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2012-11-01 | Physica D: Nonlinear Phenomena |