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Existence of unbounded solutions of a linear homogenous system of differential equations with two delays
1. | Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering and Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Brno, Czech Republic |
2. | Department of Mathematics, University of Žilina, Žilina, Slovak Republic, Slovak Republic |
References:
[1] |
O. Arino and M. Pituk, More on linear differential systems with small delays, J. Diff. Equat., 170 (2001), 381-407.
doi: 10.1006/jdeq.2000.3824. |
[2] |
F. V. Atkinson and J. R. Haddock, Criteria for asymptotic constancy of solutions of functional differential equations, J. Math. Anal. Appl., 91 (1983), 410-423.
doi: 10.1016/0022-247X(83)90161-0. |
[3] |
H. Bereketoǧlu and A. Huseynov, Convergence of solutions of nonhomogeneous linear difference systems with delays, Acta Appl. Math., 110 (2010), 259-269.
doi: 10.1007/s10440-008-9404-2. |
[4] |
H. Bereketoǧlu and F. Karakoç, Asymptotic constancy for impulsive delay differential equations, Dynam. Systems Appl., 17 (2008), 71-83. |
[5] |
H. Bereketoglu and M. Pituk, Asymptotic constancy for nonhomogeneous linear differential equations with unbounded delays, Discrete Contin. Dyn. Syst., (2003), 100-107. |
[6] |
J. Diblík, Asymptotic convergence criteria of solutions of delayed functional differential equations, J. Math. Anal. Appl., 274 (2002), 349-373.
doi: 10.1016/S0022-247X(02)00311-6. |
[7] |
J. Diblík, Asymptotic representation of solutions of equation $\dot y(t)=\beta (t)[y(t)-y(t-\tau(t))]$, J. Math. Anal. Appl., 217 (1998), 200-215.
doi: 10.1006/jmaa.1997.5709. |
[8] |
J. Diblík, R. Chupáč and M. Růžičková, Unbounded solutions of the equation $\dot y(t)=\sum_{i=1}^n\beta_i(t)[y(t-\delta_i)-y(t-\tau_i)]$, Appl. Math. Comput., 221 (2013), 610-619.
doi: 10.1016/j.amc.2013.07.001. |
[9] |
J. Diblík and M. Růžičková, Convergence of the solutions of the equation $\dot y(t)=\beta (t)[y(t-\delta)-y(t-\tau)]$ in the critical case, J. Math. Anal. Appl., 331 (2007), 1361-1370.
doi: 10.1016/j.jmaa.2006.10.001. |
[10] |
J. Diblík and M. Růžičková, Exponential solutions of equation $\dot y(t)=\beta (t)[y(t-\delta)-y(t-\tau)]$, J. Math. Anal. Appl., 294 (2004), 273-287.
doi: 10.1016/j.jmaa.2004.02.036. |
[11] |
J. Diblík, M. Růžičková and Z. Šutá, Asymptotic convergence of the solutions of a discrete system with delays, Appl. Math. Comput., 219 (2012), 4036-4044.
doi: 10.1016/j.amc.2012.10.040. |
[12] |
I. Györi and L. Horváth, Asymptotic constancy in linear difference equations: Limit formulae and sharp conditions, Adv. Difference Equ., 2010, Art. ID 789302, 20 pp. |
[13] |
I. Györi, F. Karakoç and H. Bereketoǧlu, Convergence of solutions of a linear impulsive differential equations system with many delays, Dyn. Contin. Discrete Impuls. Syst., 18 (2011), 191-202. |
[14] |
H. L. Smith, Monotone Dynamical Systems. An Introduction to the Theory of Competitive and Cooperative Systems, Mathematical Surveys and Monographs, 41, Amer. Math. Soc., Providence, 1995. |
show all references
References:
[1] |
O. Arino and M. Pituk, More on linear differential systems with small delays, J. Diff. Equat., 170 (2001), 381-407.
doi: 10.1006/jdeq.2000.3824. |
[2] |
F. V. Atkinson and J. R. Haddock, Criteria for asymptotic constancy of solutions of functional differential equations, J. Math. Anal. Appl., 91 (1983), 410-423.
doi: 10.1016/0022-247X(83)90161-0. |
[3] |
H. Bereketoǧlu and A. Huseynov, Convergence of solutions of nonhomogeneous linear difference systems with delays, Acta Appl. Math., 110 (2010), 259-269.
doi: 10.1007/s10440-008-9404-2. |
[4] |
H. Bereketoǧlu and F. Karakoç, Asymptotic constancy for impulsive delay differential equations, Dynam. Systems Appl., 17 (2008), 71-83. |
[5] |
H. Bereketoglu and M. Pituk, Asymptotic constancy for nonhomogeneous linear differential equations with unbounded delays, Discrete Contin. Dyn. Syst., (2003), 100-107. |
[6] |
J. Diblík, Asymptotic convergence criteria of solutions of delayed functional differential equations, J. Math. Anal. Appl., 274 (2002), 349-373.
doi: 10.1016/S0022-247X(02)00311-6. |
[7] |
J. Diblík, Asymptotic representation of solutions of equation $\dot y(t)=\beta (t)[y(t)-y(t-\tau(t))]$, J. Math. Anal. Appl., 217 (1998), 200-215.
doi: 10.1006/jmaa.1997.5709. |
[8] |
J. Diblík, R. Chupáč and M. Růžičková, Unbounded solutions of the equation $\dot y(t)=\sum_{i=1}^n\beta_i(t)[y(t-\delta_i)-y(t-\tau_i)]$, Appl. Math. Comput., 221 (2013), 610-619.
doi: 10.1016/j.amc.2013.07.001. |
[9] |
J. Diblík and M. Růžičková, Convergence of the solutions of the equation $\dot y(t)=\beta (t)[y(t-\delta)-y(t-\tau)]$ in the critical case, J. Math. Anal. Appl., 331 (2007), 1361-1370.
doi: 10.1016/j.jmaa.2006.10.001. |
[10] |
J. Diblík and M. Růžičková, Exponential solutions of equation $\dot y(t)=\beta (t)[y(t-\delta)-y(t-\tau)]$, J. Math. Anal. Appl., 294 (2004), 273-287.
doi: 10.1016/j.jmaa.2004.02.036. |
[11] |
J. Diblík, M. Růžičková and Z. Šutá, Asymptotic convergence of the solutions of a discrete system with delays, Appl. Math. Comput., 219 (2012), 4036-4044.
doi: 10.1016/j.amc.2012.10.040. |
[12] |
I. Györi and L. Horváth, Asymptotic constancy in linear difference equations: Limit formulae and sharp conditions, Adv. Difference Equ., 2010, Art. ID 789302, 20 pp. |
[13] |
I. Györi, F. Karakoç and H. Bereketoǧlu, Convergence of solutions of a linear impulsive differential equations system with many delays, Dyn. Contin. Discrete Impuls. Syst., 18 (2011), 191-202. |
[14] |
H. L. Smith, Monotone Dynamical Systems. An Introduction to the Theory of Competitive and Cooperative Systems, Mathematical Surveys and Monographs, 41, Amer. Math. Soc., Providence, 1995. |
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