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Periodic solutions of first order systems
On Poisson's statedependent 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, (1995). Google Scholar 
[2] 
J. K. Hale and S. M. Verduyn Lunel, "Introduction to Functional Differential Equations,", Springer, (1993). Google Scholar 
[3] 
F. Hartung, Linearized stability for a class of neutral functional differential equations with statedependent delays,, Journal of Nonlinear Analysis: Theory, 69 (2008), 1629. Google Scholar 
[4] 
F. Hartung, T. Krisztin, H. O. Walther and J. H. Wu, Functional differential equations with statedependent delays: Theory and applications, in "Handbook of Differential Equations: Ordinary Differential Equations,", Vol. III, (2006), 435. Google Scholar 
[5] 
M. C. Irwin, "Smooth Dynamical Systems,", Academic Press, (1980). Google Scholar 
[6] 
M. C. Mackey, Commodity price fluctuations:pricedependent delays and nonlinearities as explanatory factors,, J. Economic Theory, 48 (1989), 497. Google Scholar 
[7] 
M. C. Mackey, personal, communication, (2011). Google Scholar 
[8] 
S. D. Poisson, Sur les équations auxdifférences melées,, Journal de l'Ecole Polytechnique, VI (1806), 126. Google Scholar 
[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. doi: 10.1016/j.jde.2003.07.001. Google Scholar 
[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), 4055, Moscow State Aviation Institute (MAI),, Moscow 2003, 124 (2004), 5193. doi: 10.1023/B:JOTH.0000047253.23098.12. Google Scholar 
[11] 
H. O. Walther, Algebraicdelay differential systems, statedependent delay, and temporal orderof reactions,, J. Dynamics and Differential Eqs., 21 (2009), 195. doi: 10.1007/s1088400991296. Google Scholar 
[12] 
H. O. Walther, Semiflows for neutral equations with statedependent delays,, Fields Inst. Communications, (). Google Scholar 
[13] 
H. O. Walther, Linearized stability for semiflows generated by a class of neutral equations, with applications to statedependent delays,, Journal of Dynamics and Differential Equations, 22 (2010), 439. doi: 10.1007/s108840109168z. Google Scholar 
[14] 
H. O. Walther, Differential equations with locally bounded delay,, J. Differential Equations, 252 (2012), 3001. Google Scholar 
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, (1995). Google Scholar 
[2] 
J. K. Hale and S. M. Verduyn Lunel, "Introduction to Functional Differential Equations,", Springer, (1993). Google Scholar 
[3] 
F. Hartung, Linearized stability for a class of neutral functional differential equations with statedependent delays,, Journal of Nonlinear Analysis: Theory, 69 (2008), 1629. Google Scholar 
[4] 
F. Hartung, T. Krisztin, H. O. Walther and J. H. Wu, Functional differential equations with statedependent delays: Theory and applications, in "Handbook of Differential Equations: Ordinary Differential Equations,", Vol. III, (2006), 435. Google Scholar 
[5] 
M. C. Irwin, "Smooth Dynamical Systems,", Academic Press, (1980). Google Scholar 
[6] 
M. C. Mackey, Commodity price fluctuations:pricedependent delays and nonlinearities as explanatory factors,, J. Economic Theory, 48 (1989), 497. Google Scholar 
[7] 
M. C. Mackey, personal, communication, (2011). Google Scholar 
[8] 
S. D. Poisson, Sur les équations auxdifférences melées,, Journal de l'Ecole Polytechnique, VI (1806), 126. Google Scholar 
[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. doi: 10.1016/j.jde.2003.07.001. Google Scholar 
[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), 4055, Moscow State Aviation Institute (MAI),, Moscow 2003, 124 (2004), 5193. doi: 10.1023/B:JOTH.0000047253.23098.12. Google Scholar 
[11] 
H. O. Walther, Algebraicdelay differential systems, statedependent delay, and temporal orderof reactions,, J. Dynamics and Differential Eqs., 21 (2009), 195. doi: 10.1007/s1088400991296. Google Scholar 
[12] 
H. O. Walther, Semiflows for neutral equations with statedependent delays,, Fields Inst. Communications, (). Google Scholar 
[13] 
H. O. Walther, Linearized stability for semiflows generated by a class of neutral equations, with applications to statedependent delays,, Journal of Dynamics and Differential Equations, 22 (2010), 439. doi: 10.1007/s108840109168z. Google Scholar 
[14] 
H. O. Walther, Differential equations with locally bounded delay,, J. Differential Equations, 252 (2012), 3001. Google Scholar 
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