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On Poisson's state-dependent delay
1. | Mathematisches Institut, Universität Gießen, Arndtstr. 2, D 35392 Gießen, Germany |
References:
[1] |
O. Diekmann, S. A. van Gils, S. M. Verduyn Lunel and H. O. Walther, "Delay Equations: Functional-, Complex- and Nonlinear Analysis," Springer, New York, 1995. |
[2] |
J. K. Hale and S. M. Verduyn Lunel, "Introduction to Functional Differential Equations," Springer, New York, 1993. |
[3] |
F. Hartung, Linearized stability for a class of neutral functional differential equations with state-dependent delays, Journal of Nonlinear Analysis: Theory, Methods and Applications, 69 (2008), 1629-1643. |
[4] |
F. Hartung, T. Krisztin, H. O. Walther and J. H. Wu, Functional differential equations with state-dependent delays: Theory and applications, in "Handbook of Differential Equations: Ordinary Differential Equations," Vol. III, 435-545, Elsevier/North-Holland, Amsterdam, 2006. |
[5] |
M. C. Irwin, "Smooth Dynamical Systems," Academic Press, London, 1980. |
[6] |
M. C. Mackey, Commodity price fluctuations:price-dependent delays and nonlinearities as explanatory factors, J. Economic Theory, 48 (1989), 497-509. |
[7] | |
[8] |
S. D. Poisson, Sur les équations auxdifférences melées, Journal de l'Ecole Polytechnique, Tome, VI (1806), 126-147. |
[9] |
H. O. Walther, The solution manifold and $C^1$-smoothness of solution operators for differential equations with statedependent delay, J. Differential Eqs., 195 (2003), 46-65.
doi: 10.1016/j.jde.2003.07.001. |
[10] |
H. O. Walther, Smoothness properties of semiflows for differential equations with state dependent delay, in "Proceedings of the International Conference on Differential and Functional Differential Equations, Moscow, 2002," 1 (2002), 40-55, Moscow State Aviation Institute (MAI), Moscow 2003, English version: Journal of the Mathematical Sciences, 124 (2004), 5193-5207.
doi: 10.1023/B:JOTH.0000047253.23098.12. |
[11] |
H. O. Walther, Algebraic-delay differential systems, state-dependent delay, and temporal orderof reactions, J. Dynamics and Differential Eqs., 21 (2009), 195-232.
doi: 10.1007/s10884-009-9129-6. |
[12] |
H. O. Walther, Semiflows for neutral equations with state-dependent delays,, Fields Inst. Communications, ().
|
[13] |
H. O. Walther, Linearized stability for semiflows generated by a class of neutral equations, with applications to state-dependent delays, Journal of Dynamics and Differential Equations, 22 (2010), 439-462.
doi: 10.1007/s10884-010-9168-z. |
[14] |
H. O. Walther, Differential equations with locally bounded delay, J. Differential Equations, 252 (2012), 3001-3039. |
show all references
References:
[1] |
O. Diekmann, S. A. van Gils, S. M. Verduyn Lunel and H. O. Walther, "Delay Equations: Functional-, Complex- and Nonlinear Analysis," Springer, New York, 1995. |
[2] |
J. K. Hale and S. M. Verduyn Lunel, "Introduction to Functional Differential Equations," Springer, New York, 1993. |
[3] |
F. Hartung, Linearized stability for a class of neutral functional differential equations with state-dependent delays, Journal of Nonlinear Analysis: Theory, Methods and Applications, 69 (2008), 1629-1643. |
[4] |
F. Hartung, T. Krisztin, H. O. Walther and J. H. Wu, Functional differential equations with state-dependent delays: Theory and applications, in "Handbook of Differential Equations: Ordinary Differential Equations," Vol. III, 435-545, Elsevier/North-Holland, Amsterdam, 2006. |
[5] |
M. C. Irwin, "Smooth Dynamical Systems," Academic Press, London, 1980. |
[6] |
M. C. Mackey, Commodity price fluctuations:price-dependent delays and nonlinearities as explanatory factors, J. Economic Theory, 48 (1989), 497-509. |
[7] | |
[8] |
S. D. Poisson, Sur les équations auxdifférences melées, Journal de l'Ecole Polytechnique, Tome, VI (1806), 126-147. |
[9] |
H. O. Walther, The solution manifold and $C^1$-smoothness of solution operators for differential equations with statedependent delay, J. Differential Eqs., 195 (2003), 46-65.
doi: 10.1016/j.jde.2003.07.001. |
[10] |
H. O. Walther, Smoothness properties of semiflows for differential equations with state dependent delay, in "Proceedings of the International Conference on Differential and Functional Differential Equations, Moscow, 2002," 1 (2002), 40-55, Moscow State Aviation Institute (MAI), Moscow 2003, English version: Journal of the Mathematical Sciences, 124 (2004), 5193-5207.
doi: 10.1023/B:JOTH.0000047253.23098.12. |
[11] |
H. O. Walther, Algebraic-delay differential systems, state-dependent delay, and temporal orderof reactions, J. Dynamics and Differential Eqs., 21 (2009), 195-232.
doi: 10.1007/s10884-009-9129-6. |
[12] |
H. O. Walther, Semiflows for neutral equations with state-dependent delays,, Fields Inst. Communications, ().
|
[13] |
H. O. Walther, Linearized stability for semiflows generated by a class of neutral equations, with applications to state-dependent delays, Journal of Dynamics and Differential Equations, 22 (2010), 439-462.
doi: 10.1007/s10884-010-9168-z. |
[14] |
H. O. Walther, Differential equations with locally bounded delay, J. Differential Equations, 252 (2012), 3001-3039. |
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