@article{a012962fd26d4b9bb015a14156685f77,

title = "Liapunov exponents for higher-order linear differential equations whose characteristic equations have variable real roots",

abstract = "We consider the linear differential equation Σk=0 naak(t)x(n-k)(t) = 0 t ≥ 0, n≥2, where a0(t) ≡ 1, ak(t) are continuous bounded functions. Assuming that all the roots of the polynomial zn + a1 (t)zn-1 + ⋯ + a n(t) are real and satisfy the inequality rk(t) < γ for t ≥ 0 and k = 1,..., n, we prove that the solutions of the above equation satisfy |x(i)| ≤ const eγt for t ≥ 0.",

keywords = "Exponential stability, Liapunov exponents, Linear differential equations",

author = "Gil, {Michael I.}",

note = "Funding Information: Generous financial support from the Swedish Natural Science Research Council (Vetenskapsr{\aa}det), the Swedish Strategic Research Foundation (Stiftelsen f{\"o}r Strategisk Forskning), European Union Biotechnology Program (LSHB-CT-2004-005276, Contract No. 005276), and Philip Morris USA, Inc. is gratefully acknowledged. The computational resources have been granted by the Swedish National Allocation Committee for the High Performance Computing and provided by the National Supercomputer Center (Link{\"o}ping, Sweden) for what the authors are thankful for.",

year = "2008",

month = apr,

day = "15",

language = "English",

volume = "2008",

pages = "1--6",

journal = "Electronic Journal of Differential Equations",

issn = "1072-6691",

publisher = "Texas State University - San Marcos",

}