Seminar on Qualitative Theory of Differential Equations - Mihály Pituk (1.12.2016)
Thursday 1.12.2016 at 14:00, Lecture room M-223
By: Pavol Quittner
Mihály Pituk (University of Pannonia, Veszprém):
Lyapunov Exponents of Positive Solutions of a Perturbed System of Delay Differential Equations
We will consider perturbations of a linear system of autonomous delay differential equations. According to a Perron type theorem, if the Lyapunov exponent of a solution is finite, then it is equal to the real part of one of the eigenvalues of the unperturbed linear part. In this talk we will show that if in addition the solution is positive then its Lyapunov exponent is a real eigenvalue of the linear part with a positive eigenfunction.