On time transformations for differential equations with state-dependent delay

 Access to full text

 Full (PDF)

1. [1] Arino O., Hadeler K.P., Hbid M.L., Existence of periodic solutions for delay differential equations with state dependent delay, J. Differential Equations, 1998, 144(2), 263–301 http://dx.doi.org/10.1006/jdeq.1997.3378 
2. [2] Brunner H., Maset S., Time transformations for delay differential equations, Discrete Contin. Dyn. Syst., 2009, 25(3), 751–775 http://dx.doi.org/10.3934/dcds.2009.25.751 Zbl1187.34093
3. [3] Brunner H., Maset S., Time transformations for state-dependent delay differential equations, Commun. Pure Appl. Anal., 2010, 9(1), 23–45 http://dx.doi.org/10.3934/cpaa.2010.9.23 Zbl1194.34135
4. [4] Chepyzhov V.V., Vishik M.I., Appendix: Non-authonomous dynamical systems and their attractors, In: Vishik M.I., Asymptotic Behaviour of Solutions of Evolutionary Equations, Lezioni Lincee, Cambridge University Press, Cambridge, 1992 
5. [5] Chueshov I.D., Introduction to the Theory of Infinite-Dimensional Dissipative Systems, Univ. Lektsii Sovrem. Mat., ACTA, Kharkov, 1999 (in Russian); English translation available at http://www.emis.de/monographs/Chueshov/ Zbl1100.37046
6. [6] Diekmann O., van Gils S.A., Verduyn Lunel S.M., Walther H.-O., Delay Equations, Appl. Math. Sci., 110, Springer, New York, 1995 http://dx.doi.org/10.1007/978-1-4612-4206-2 
7. [7] Hale J., Theory of Functional Differential Equations, 2nd ed., Appl. Math. Sci., 3, Springer, Heidelberg-New York, 1977 http://dx.doi.org/10.1007/978-1-4612-9892-2 
8. [8] Hale J.K., Asymptotic Behavior of Dissipative Systems, Math. Surveys Monogr., 25, American Mathematical Society, Providence, 1988 Zbl0642.58013
9. [9] Hartung F., Krisztin T., Walther H.-O., Wu J., Functional differential equations with state-dependent delays: Theory and applications, In: Handbook of Differential Equations: Ordinary Differential Equations, III, Handb. Differ. Equ., Elsevier/North Holland, 2006, Amsterdam, 435–545 http://dx.doi.org/10.1016/S1874-5725(06)80009-X 
10. [10] Krisztin T., A local unstable manifold for differential equations with state-dependent delay, Discrete Contin. Dyn. Syst., 2003, 9(4), 993–1028 http://dx.doi.org/10.3934/dcds.2003.9.993 Zbl1048.34123
11. [11] Mallet-Paret J., Nussbaum R.D., Paraskevopoulos P., Periodic solutions for functional-differential equations with multiple state-dependent time lags, Topol. Methods Nonlinear Anal., 1994, 3(1), 101–162 Zbl0808.34080
12. [12] Rezounenko A.V., Differential equations with discrete state-dependent delay: uniqueness and well-posedness in the space of continuous functions, Nonlinear Anal., 2009, 70(11), 3978–3986 http://dx.doi.org/10.1016/j.na.2008.08.006 Zbl1163.35494
13. [13] Rezounenko A.V., A condition on delay for differential equations with discrete state-dependent delay, J. Math. Anal. Appl., 2012, 385(1), 506–516 http://dx.doi.org/10.1016/j.jmaa.2011.06.070 Zbl1242.34136
14. [14] Temam R., Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Appl. Math. Sci., 68, Springer, New York, 1988 http://dx.doi.org/10.1007/978-1-4684-0313-8 
15. [15] Vorotnikov V.I., Rumyantsev V.V., Stability and Control with Respect to Part of the Coordinates of the Phase Vector of Dynamical Systems: Theory, Methods and Applications, Nauchnyi Mir, Moscow, 2001 (in Russian) Zbl1016.34052
16. [16] Walther H.-O., The solution manifold and C 1-smoothness for differential equations with state-dependent delay, J. Differential Equations, 2003, 195(1), 46–65 http://dx.doi.org/10.1016/j.jde.2003.07.001 Zbl1045.34048