MMN-2736

In the first part of this work we present some basics about the connection of exponential dichotomy and Floquet-theory. After that we are going to study some stability notions of linear differential equations based on the concept of the exponential and ordinary dichotomy. More precisely we are going to see how we can generalize the definition of the asymptotical (Lyapunov-) stability using the exponential dichotomy. In the main part of the paper we consider parameter dependent non-autonomous linear and autonomous nonlinear systems which have at a certain value of the parameter an asymptotically stable solution. Then we examine the question how much the parameter can change in order the solution remains asymptotically stable. Finally, we study the orbital stability of periodic solutions of autonomous systems applying the previous results.

Vol. 20 (2019), No. 1, pp. 353-364

DOI: 10.18514/MMN.2019.2736

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