Seminár z kvalitatívnej teórie diferenciálnych rovníc

Seminar on Qualitative Theory of Differential Equations

Thursday 1.12.2016 at 14:00 Lecture room M-223

Mihály Pituk (University of Pannonia, Veszprém):

Lyapunov Exponents of Positive Solutions

of a Perturbed System of Delay Differential Equations

Abstract:

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.