Periodic solutions to differential equations with delay
Periodic solutions to differential equations with delay
The authors describe an approach for establishing the existence of periodic solutions to the differential system with delay \[ z'(t)- Az(t)- Bz(t-\tau)= F(z(t)), \] where \(A\) and \(B\) are \(m\times m\) constant matrices, \(\tau>0\), \(F:\mathbb{R}^m\to\mathbb{R}^m\) is continuous. The approach is based on ideas from the method of harmonic balance to locate a center for a ball to which Schauder's theorem can be applied. The method extends easily to problems with several delays.
- University of Florence Italy
- University of Siena Italy
delay, periodic solutions, harmonic balance, Periodic solutions to ordinary differential equations, Periodic solutions to functional-differential equations, Theoretical approximation of solutions to ordinary differential equations
delay, periodic solutions, harmonic balance, Periodic solutions to ordinary differential equations, Periodic solutions to functional-differential equations, Theoretical approximation of solutions to ordinary differential equations
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