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Global solutions of a Keller--Segel system with saturated logarithmic sensitivity function
On the asymptotic stability of Volterra functional equations with vanishing delays
| 1. | Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong SAR |
| 2. | Department of Mathematics and Statistics, Memorial University of Newfoundland, St.Johns, Newfoundland, A1C 5S7 |
References:
| [1] |
A. Bellen and M. Zennaro, Numerical Methods for Delay Differential Equations, Clarendon Press, Oxford, 2003.
doi: 10.1093/acprof:oso/9780198506546.001.0001. |
| [2] |
H. Brunner, The numerical analysis of functional integral and integro-differential equations of Volterra type, Acta Numer., 13 (2004), 55-145.
doi: 10.1017/CBO9780511569975.002. |
| [3] |
H. Brunner, Current work and open problems in the numerical analysis of Volterra functional equations with vanishing delays, Front. Math. China, 4 (2009), 3-22.
doi: 10.1007/s11464-009-0001-0. |
| [4] |
H. Brunner and H. Liang, Stability of collocation methods for delay differential equations with vanishing delays, BIT Numer. Math., 50 (2010), 693-711.
doi: 10.1007/s10543-010-0285-1. |
| [5] |
A. Iserles, On the generalized pantograph functional differential equation, Europ. J. Appl. Math., 4 (1993), 1-38.
doi: 10.1017/S0956792500000966. |
| [6] |
A. Iserles and J. Terjéki, Stability and asymptotic stability of functional-differential equations, J. London Math. Soc., 51 (1995), 559-572.
doi: 10.1112/jlms/51.3.559. |
| [7] |
T. Kato and J. B. McLeod, The functional-differential equation $y'(x)=ay(\lambda x)+by(x)$, Bull. Amer. Math. Soc., 77 (1970), 891-937. |
show all references
References:
| [1] |
A. Bellen and M. Zennaro, Numerical Methods for Delay Differential Equations, Clarendon Press, Oxford, 2003.
doi: 10.1093/acprof:oso/9780198506546.001.0001. |
| [2] |
H. Brunner, The numerical analysis of functional integral and integro-differential equations of Volterra type, Acta Numer., 13 (2004), 55-145.
doi: 10.1017/CBO9780511569975.002. |
| [3] |
H. Brunner, Current work and open problems in the numerical analysis of Volterra functional equations with vanishing delays, Front. Math. China, 4 (2009), 3-22.
doi: 10.1007/s11464-009-0001-0. |
| [4] |
H. Brunner and H. Liang, Stability of collocation methods for delay differential equations with vanishing delays, BIT Numer. Math., 50 (2010), 693-711.
doi: 10.1007/s10543-010-0285-1. |
| [5] |
A. Iserles, On the generalized pantograph functional differential equation, Europ. J. Appl. Math., 4 (1993), 1-38.
doi: 10.1017/S0956792500000966. |
| [6] |
A. Iserles and J. Terjéki, Stability and asymptotic stability of functional-differential equations, J. London Math. Soc., 51 (1995), 559-572.
doi: 10.1112/jlms/51.3.559. |
| [7] |
T. Kato and J. B. McLeod, The functional-differential equation $y'(x)=ay(\lambda x)+by(x)$, Bull. Amer. Math. Soc., 77 (1970), 891-937. |
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