TY - JOUR
T1 - On the asymptotics of solutions of a class of linear functional-differential equations
AU - Derfel, G.
AU - Vogl, F.
PY - 1996/1/1
Y1 - 1996/1/1
N2 - A sharp estimate of the growth of solutions of the initial value problem for systems of the form u̇(t) = ∑lj=1 Cj(t) u(λj t), t ≥ t0 > 0, 0 < λj < 1, u(t) = φ(t) for λt0 ≤ t ≤ t0, λ = min λj, where Cj(t) are matrices with elements of power growth, is found. As a corollary of this result, it follows, for instance, that each solution of the initial value problem satisfies the estimate ∥u(t)∥ ≤ C exp{γln2(1 + |t|)} for some C > 0 and γ > 0.
AB - A sharp estimate of the growth of solutions of the initial value problem for systems of the form u̇(t) = ∑lj=1 Cj(t) u(λj t), t ≥ t0 > 0, 0 < λj < 1, u(t) = φ(t) for λt0 ≤ t ≤ t0, λ = min λj, where Cj(t) are matrices with elements of power growth, is found. As a corollary of this result, it follows, for instance, that each solution of the initial value problem satisfies the estimate ∥u(t)∥ ≤ C exp{γln2(1 + |t|)} for some C > 0 and γ > 0.
UR - http://www.scopus.com/inward/record.url?scp=0040821594&partnerID=8YFLogxK
U2 - 10.1017/s0956792500002527
DO - 10.1017/s0956792500002527
M3 - Article
AN - SCOPUS:0040821594
SN - 0956-7925
VL - 7
SP - 511
EP - 518
JO - European Journal of Applied Mathematics
JF - European Journal of Applied Mathematics
IS - 5
ER -