Geodesic
On upward mobility of the highest exponent of a linear differential system under perturbations of the coefficients from the simplest classes with degeneracies
Trudy Instituta matematiki, Tome 25 (2017) no. 2, pp. 50-59

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We obtain some upper bound for the highest exponent of a linear differential system with perturbation matrix $Q$, satisfying the condition $\|Q (t)\|\le N_Q\beta(t)$, $t\ge0$, where $N_Q>0$ is some constant depending on $Q$, and $\beta$ is an arbitrary fixed nonnegative piecewise continuous bounded function that is infinitesimal in the mean on the positive semiaxis. 
@article{TIMB_2017_25_2_a4,
     author = {E. K. Makarov and I. V. Marchenko},
     title = {On upward mobility of the highest exponent of a linear differential system under perturbations of the coefficients from the simplest classes with degeneracies},
     journal = {Trudy Instituta matematiki},
     pages = {50--59},
     publisher = {mathdoc},
     volume = {25},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMB_2017_25_2_a4/}
}
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E. K. Makarov; I. V. Marchenko. On upward mobility of the highest exponent of a linear differential system under perturbations of the coefficients from the simplest classes with degeneracies. Trudy Instituta matematiki, Tome 25 (2017) no. 2, pp. 50-59. http://geodesic.mathdoc.fr/item/TIMB_2017_25_2_a4/