caa a22 4500 605523940 CHVBK 20210128100751.0 cr unu---uuuuu 210128e20151001xx s 000 0 eng 10.1007/s10958-015-2557-4 doi (NATIONALLICENCE)springer-10.1007/s10958-015-2557-4 Erchenko A. Pennsylvania State University, University Park, 16801, State College, PA, United States aut Lyapunov Reducibility of Infinitesimal Perturbations of Equations and Systems [Elektronische Daten] [A. Erchenko] We consider two classes of infinitesimally small perturbations of a given linear differential equation with continuous, possibly unbounded, coefficients. The first class consists of its perturbations in the space of all linear systems and the second class consists of perturbations with somewhat slower decay but in a narrower space, namely the space of systems corresponding to single equations. It is shown that the values of a Lyapunov invariant functional on the first class belong to the range of the same functional on the second class. For systems with bounded coefficients, it is shown that the said sets coincide. Springer Science+Business Media New York, 2015 Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 210/2(2015-10-01), 200-209 1072-3374 210:2<200 2015 210 10958 https://doi.org/10.1007/s10958-015-2557-4 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10958-015-2557-4 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Erchenko A. Pennsylvania State University, University Park, 16801, State College, PA, United States aut NATIONALLICENCE 773 0- Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 210/2(2015-10-01), 200-209 1072-3374 210:2<200 2015 210 10958