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Direct exponential ordering for neutral compartmental systems with nonautonomous $\mathbf{D}$operator
1.  Departamento de Matemática Aplicada, Escuela de Ingenierías Industriales and member of IMUVA, Instituto de Matemáticas, Universidad de Valladolid, 47011 Valladolid, Spain 
2.  Departamento de Matemática Aplicada, Escuela de Ingenierías Industriales, Universidad de Valladolid, 47011 Valladolid, Spain 
References:
[1] 
O. Arino and F. Bourad, On the asymptotic behavior of the solutions of a class of scalar neutral equations generating a monotone semiflow, J. Differential Equations, 87 (1990), 8495. 
[2] 
O. Arino and E. Haourigui, On the asymptotic behavior of solutions of some delay differential systems which have a first integral, J. Math. Anal. Appl., 122 (1987), 3646. doi: 10.1016/0022247X(87)903428. 
[3] 
R. Ellis, "Lectures on Topological Dynamics," Benjamin, New York, 1969. 
[4] 
A. M. Fink, "Almost Periodic Differential Equations," Lecture Notes in Mathematics SpringerVerlag, Berlin, Heidelberg, New York, 377 (1974), viii+336 pp. 
[5] 
I. Gy\Hori, Connections between compartmental systems with pipes and integrodifferential equations, Math. Modelling, 7 (1986), 12151238. doi: 10.1016/02700255(86)900771. 
[6] 
I. Gy\Hori and J. Eller, Compartmental systems with pipes, Math. Biosci., 53 (1981), 223247. doi: 10.1016/00255564(81)900195. 
[7] 
I. Gy\Hori and J. Wu, A neutral equation arising from compartmental systems with pipes, J. Dynam. Differential Equations, 3 (1991), 289311. 
[8] 
W. M. Haddad, V. Chellaboina and Q. Hui, "Nonnegative and Compartmental Dynamical Systems," Princeton University Press, 2010. 
[9] 
J. K. Hale, "Theory of Functional Differential Equations," Applied Mathematical Sciences vol. 3, SpringerVerlag, Berlin, Heidelberg, New York, 1977. 
[10] 
J. K. Hale and S. M. Verduyn Lunel, "Introduction to Functional Differential Equations," Applied Mathematical Sciences vol. 99, SpringerVerlag, Berlin, Heidelberg, New York, 1993. 
[11] 
Y. Hino, S. Murakami and T. Naito, "Functional Differential Equations with Infinite Delay," Lecture Notes in Math., vol. 1473, SpringerVerlag, Berlin, Heidelberg, 1991. 
[12] 
J. A. Jacquez, "Compartmental Analysis in Biology and Medicine," Third Edition, ThomsonShore Inc., Ann Arbor, Michigan, 1996. 
[13] 
J. A. Jacquez and C. P. Simon, Qualitative theory of compartmental systems, SIAM Review, 35 (1993), 4379. doi: 10.1137/1035003. 
[14] 
J. Jiang and X.Q. Zhao, Convergence in monotone and uniformly stable skewproduct semiflows with applications, J. Reine Angew. Math., 589 (2005), 2155. doi: 10.1515/crll.2005.2005.589.21. 
[15] 
T. Krisztin and J. Wu, Asymptotic periodicity, monotonicity, and oscillation of solutions of scalar neutral functional differential equations, J. Math. Anal. Appl., 199 (1996), 502525. doi: 10.1006/jmaa.1996.0158. 
[16] 
V. Mu\ nozVillarragut, S. Novo and R. Obaya, Neutral functional differential equations with applications to compartmental systems, SIAM J. Math. Anal., 40 (2008), 10031028. doi: 10.1137/070711177. 
[17] 
S. Novo, R. Obaya and A. M. Sanz, Stability and extensibility results for abstract skewproduct semiflows, J. Differential Equations, 235 (2007), 623646. 
[18] 
S. Novo, R. Obaya and V. M. Villarragut, Exponential ordering for nonautonomous neutral functional differential equations, SIAM J. Math. Anal., 41 (2009), 10251053. doi: 10.1137/080744682. 
[19] 
R. Obaya and V. M. Villarragut, Exponential ordering for neutral functional differential equations with nonautonomous linear $D$operator, J. Dyn. Diff. Equat., 23 (2011), 695725. doi: 10.1007/s1088401192109. 
[20] 
R. J. Sacker and G. R. Sell, "Lifting Properties in SkewProducts Flows with Applications to Differential Equations," Mem. Amer. Math. Soc., vol. 190, Amer. Math. Soc., Providence, 1977. 
[21] 
W. X. Shen and Y. F. Yi, "Almost Automorphic and Almost Periodic Dynamics in SkewProduct Semiflows," Mem. Amer. Math. Soc., 136 (1998), x+93 pp. 
[22] 
Z. Wang and J. Wu, Neutral functional differential equations with infinite delay, Funkcial. Ekvac., 28 (1985), 157170. 
[23] 
J. Wu, Unified treatment of local theory of NFDEs with infinite delay, Tamkang J. Math., 22 (1991), 5172. 
[24] 
J. Wu and H. I. Freedman, Monotone semiflows generated by neutral functional differential equations with application to compartmental systems, Can. J. Math., 43 (1991), 10981120. doi: 10.4153/CJM19910641. 
show all references
References:
[1] 
O. Arino and F. Bourad, On the asymptotic behavior of the solutions of a class of scalar neutral equations generating a monotone semiflow, J. Differential Equations, 87 (1990), 8495. 
[2] 
O. Arino and E. Haourigui, On the asymptotic behavior of solutions of some delay differential systems which have a first integral, J. Math. Anal. Appl., 122 (1987), 3646. doi: 10.1016/0022247X(87)903428. 
[3] 
R. Ellis, "Lectures on Topological Dynamics," Benjamin, New York, 1969. 
[4] 
A. M. Fink, "Almost Periodic Differential Equations," Lecture Notes in Mathematics SpringerVerlag, Berlin, Heidelberg, New York, 377 (1974), viii+336 pp. 
[5] 
I. Gy\Hori, Connections between compartmental systems with pipes and integrodifferential equations, Math. Modelling, 7 (1986), 12151238. doi: 10.1016/02700255(86)900771. 
[6] 
I. Gy\Hori and J. Eller, Compartmental systems with pipes, Math. Biosci., 53 (1981), 223247. doi: 10.1016/00255564(81)900195. 
[7] 
I. Gy\Hori and J. Wu, A neutral equation arising from compartmental systems with pipes, J. Dynam. Differential Equations, 3 (1991), 289311. 
[8] 
W. M. Haddad, V. Chellaboina and Q. Hui, "Nonnegative and Compartmental Dynamical Systems," Princeton University Press, 2010. 
[9] 
J. K. Hale, "Theory of Functional Differential Equations," Applied Mathematical Sciences vol. 3, SpringerVerlag, Berlin, Heidelberg, New York, 1977. 
[10] 
J. K. Hale and S. M. Verduyn Lunel, "Introduction to Functional Differential Equations," Applied Mathematical Sciences vol. 99, SpringerVerlag, Berlin, Heidelberg, New York, 1993. 
[11] 
Y. Hino, S. Murakami and T. Naito, "Functional Differential Equations with Infinite Delay," Lecture Notes in Math., vol. 1473, SpringerVerlag, Berlin, Heidelberg, 1991. 
[12] 
J. A. Jacquez, "Compartmental Analysis in Biology and Medicine," Third Edition, ThomsonShore Inc., Ann Arbor, Michigan, 1996. 
[13] 
J. A. Jacquez and C. P. Simon, Qualitative theory of compartmental systems, SIAM Review, 35 (1993), 4379. doi: 10.1137/1035003. 
[14] 
J. Jiang and X.Q. Zhao, Convergence in monotone and uniformly stable skewproduct semiflows with applications, J. Reine Angew. Math., 589 (2005), 2155. doi: 10.1515/crll.2005.2005.589.21. 
[15] 
T. Krisztin and J. Wu, Asymptotic periodicity, monotonicity, and oscillation of solutions of scalar neutral functional differential equations, J. Math. Anal. Appl., 199 (1996), 502525. doi: 10.1006/jmaa.1996.0158. 
[16] 
V. Mu\ nozVillarragut, S. Novo and R. Obaya, Neutral functional differential equations with applications to compartmental systems, SIAM J. Math. Anal., 40 (2008), 10031028. doi: 10.1137/070711177. 
[17] 
S. Novo, R. Obaya and A. M. Sanz, Stability and extensibility results for abstract skewproduct semiflows, J. Differential Equations, 235 (2007), 623646. 
[18] 
S. Novo, R. Obaya and V. M. Villarragut, Exponential ordering for nonautonomous neutral functional differential equations, SIAM J. Math. Anal., 41 (2009), 10251053. doi: 10.1137/080744682. 
[19] 
R. Obaya and V. M. Villarragut, Exponential ordering for neutral functional differential equations with nonautonomous linear $D$operator, J. Dyn. Diff. Equat., 23 (2011), 695725. doi: 10.1007/s1088401192109. 
[20] 
R. J. Sacker and G. R. Sell, "Lifting Properties in SkewProducts Flows with Applications to Differential Equations," Mem. Amer. Math. Soc., vol. 190, Amer. Math. Soc., Providence, 1977. 
[21] 
W. X. Shen and Y. F. Yi, "Almost Automorphic and Almost Periodic Dynamics in SkewProduct Semiflows," Mem. Amer. Math. Soc., 136 (1998), x+93 pp. 
[22] 
Z. Wang and J. Wu, Neutral functional differential equations with infinite delay, Funkcial. Ekvac., 28 (1985), 157170. 
[23] 
J. Wu, Unified treatment of local theory of NFDEs with infinite delay, Tamkang J. Math., 22 (1991), 5172. 
[24] 
J. Wu and H. I. Freedman, Monotone semiflows generated by neutral functional differential equations with application to compartmental systems, Can. J. Math., 43 (1991), 10981120. doi: 10.4153/CJM19910641. 
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