MR2867016
L. BEREZANSKY, E. BRAVERMAN and A. DOMOSHNITSKY
L. BEREZANSKY, E. BRAVERMAN and A. DOMOSHNITSKY
On Nonoscillation of Systems of Delay Equations
Funkcialaj Ekvacioj. Serio Internacia
54
2011
275--296
http://fe.math.kobe-u.ac.jp/FE/FullPapers/54-2/54_275.pdf
http://www.ams.org/mathscinet-getitem?mr=MR2867016
The paper investigates nonnegativity of all entries of the fundamental matrix for the system of linear delay differential equations $\dot{X}(t)+\sum_{k=1}^m A_k(t)X(h_k(t))=0$ in the case when the non-diagonal entries of matrices $A_k$ are nonpositive. The results are applied to study nonoscillation of high order differential equations, as well as exponential stability for systems of delay equations.
Systems of delay equations, Nonoscillation, Nonnegative fundamental matrix, High order delay equations, Exponential stability.
34K11, 34K20.
54-275
2011
On Nonoscillation of Systems of Delay Equations
L. BEREZANSKY, E. BRAVERMAN and A. DOMOSHNITSKY
L. BEREZANSKY, E. BRAVERMAN and A. DOMOSHNITSKY
1
Agarwal, R. P.; Domoshnitsky, A.
On positivity of several components of solution vector for systems of linear functional differential equations
Glasg. Math. J.
52
2010
115--136
MR2587821
2
Azbelev, N.; Maksimov, V.; Rakhmatullina, L.
Introduction to the Theory of Linear Functional Differential Equations
Advanced Series in Mathematical Science and Engineering, 3,
World Federation Publishers, Atlanta
1996
MR1422013
3
Bainov, D.; Domoshnitsky, A.
Nonnegativity of the Cauchy matrix and exponential stability of a neutral type system of functional differential equations
Extracta Math.
8
1992
75--82
MR1270333
4
Beckenbach, E. F.; Bellman, R.
Inequalities
Springer-Verlag, Berlin
1971
MR0192009
5
Berezansky, L.; Braverman, E.
On non-oscillation of a scalar delay differential equation
Dynam. Systems Appl.
6
1997
567--580
MR1487479
6
Berezansky, L.; Braverman, E.
On exponential stability of linear differential equations with several delays
J. Math. Anal. Appl.
324
2006
1336--1355
MR2266563
7
Berezansky, L.; Braverman, E.
Nonoscillation and exponential stability of delay differential equations with oscillating coefficients
J. Dyn. Control Syst.
15
2009
63--82
MR2475661
8
Berman, A.; Plemmons, R. J.
Nonnegative matrices in the mathematical sciences
Academic Press, New York
1979
MR0544666
9
Chaplygin, S. A.
Foundations of new method of approximate integration of differential equations
Moscow, 1919 (Collected works 1, GosTechIzdat)
1948
348--368
10
Domoshnitsky, A.
Componentwise applicability of Chaplygin's theorem to a system of linear differential equations with delay, (Russian)
Differentsial'nye Uravneniya
26
1990
1699--1705, 1836--1837; translation in Differential Equations 26 (1990), 1254--1259
MR1089738
11
Domoshnitsky, A.; Sheina, M. V.
Nonnegativity of the Cauchy matrix and the stability of a system of linear differential equations with retarded argument, (Russian)
Differentsial'nye Uravneniya
25
1989
201--208, 360; translation in Differential Equations 25 (1989), 145--150
MR0994699
12
Engel, K.-J.; Nagel, R.
One-parameter semigroups for linear evolution equations
Graduate Texts in Mathematics, 194, Springer-Verlag, New York
2000
MR1721989
13
Gopalsamy, K.
Stability and Oscillation in Delay Differential Equations of Population Dynamics
Mathematics and its Applications, 74, Kluwer Academic Publishers, Dordrecht, Boston, London
1992
MR1163190
14
Györi, I.
Interaction between oscillations and global asymptotic stability in delay differential equations
Differential Integral Equations
3
1990
181--200
MR1014735
15
Györi, I.; Hartung, F.
Stability in delay perturbed differential and difference equations
Topics in functional differential and difference equations (Lisbon, 1999), Fields Inst. Commun., 29
2001
181--194
MR1821781
16
Györi, I.; Hartung, F.
Fundamental solution and asymptotic stability of linear delay differential equations
Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal.
13
2006
261--287
MR2204331
17
Györi, I.; Ladas, G.
Oscillation Theory of Delay Differential Equations with Applications
Oxford Mathematical Monographs, Clarendon Press, New York
1991
MR1168471
18
Ngoc, P. H. A.; Naito, T.; Shin, J. S.
Characterization of positive linear functional differential equations
Funkcial. Ekvac.
50
2007
1--17
MR2332076
2332076
19
Wazewski, T.
Systèmes des équations et des inégalités différentielles aux ordinaires aux deuxièmes membres monotones et leurs applications
Ann. Soc. Polon. Math.
23
1950
112--166
MR0040506