Positivity and stability of delay equations with nonautonomous past

Mathematische Nachrichten

Volumn 278, Issue 7-8, 2005, Pages 864-876

  Nickel, Gregor ^a   Rhandi, Abdelaziz ^b  

^a UNIVERSITY OF TÜBINGEN   (Germany)

^b FACULTÉ DES SCIENCES SEMLALIA   (Morocco)

Author keywords

Nonautonomous delay equations; Population dynamics; Positivity; Stability

Indexed keywords

EID: 20444396614     PISSN: 0025584X     EISSN: None     Source Type: Journal    
DOI: 10.1002/mana.200310278     Document Type: Article

References (21)

1. H. Amann, Dual semigroups and second order linear elliptic boundary value problems, Israel J. Math. 45, 225-254 (1983).
2. S. Brendle and R. Nagel, Partial functional differential equations with nonautonomous past, Disc. Cont. Dyn. Sys. 8, 1-14 (2002).
3. C. Chicone and Y. Latushkin, Evolution Semigroups in Dynamical Systems and Differential Equations, Mathematical Surveys and Monographs Vol. 70 (Amer. Math. Soc., Providence, R. I., 1999).
4. N. Dunford and J. T. Schwartz, Linear Operator. Part I: General Theory (Interscience Publishers, New York, 1958).
5. K. J. Engel and R. Nagel, One-parameter Semigroups for Linear Evolution Equations, Graduate Texts in Mathematics Vol. 194 (Springer-Verlag, New York, 2000).
6. G. Fragnelli and L. Tonetto, A population equation with diffusion, J. Math. Anal. Appl. 289, 90-99 (2004).
7. G. Fragnelli, Classical solutions for partial functional differential equations with nonautonomous past, Arch. Math. (Basel) 79, 479-488 (2002).
8. p -phase spaces, Diff. Int. Eq. 16, 327-348 (2003).
9. I. Gohberg, S. Goldberg, and M. A. Kaashoek, Classes of Linear Operators Vol. I (Birkhäuser-Verlag, Basel, 1990).
10. N. T. Huy, Resolvents of operators and partial functional differential equations with non-autonomous past, J. Math. Anal. Appl. 289, 301-316 (2004).
11. R. Nagel (ed.), One-parameter Semigroups of Positive Operators, Lecture Notes in Mathematics Vol. 1184 (Springer-Verlag, Berlin, 1986).
12. R. Nagel and G. Nickel, Wellposedness for nonautonomous abstract Cauchy problems, in: Progress in Nonlinear Differential Equations and their Applications Vol. 50 (Birkhäuser Verlag, Basel, 2002), pp. 279-293.
13. P. Marcati and M. A. Pozio, Global asymptotic stability for a vector disease model with spatial spread, J. Math. Biol. 9, 179-187 (1980).
14. G. Nickel, Evolution semigroups for nonautonomous Cauchy problems, Abstract Appl. Analysis 2, 73-95 (1997).
15. F. Räbiger, A. Rhandi, R. Schnaubelt, and J. Voigt, Non-autonomous Miyadera perturbation, Diff. Int. Equ. 13, 341-368 (2000).
16. 1, Disc. Cont. Dyn. Syst. 5, 663-683 (1999).
17. A. Rhandi, Spectral Theory for Positive Semigroups and Application, Quaderno del'Università di Lecce Q.I (2002).
18. H. H. Schaefer, Banach Lattices and Positive Operators (Springer-Verlag, Berlin, 1974).
19. J. Voigt, A perturbation theorem for the essential spectral radius of strongly continuous semigroups, Monatsh. Math. 90, 153-161 (1980).
20. J. Voigt, On the convex compactness property for strong operator topology, Note Mat. 12, 259-269 (1992).
21. A. C. Zaanen, Riesz Spaces II (North-Holland, Amsterdam, 1983).