Note on semilinear abstract functional differential and integrodifferential equations with infinite delay

Applied Mathematics Letters

Volumn 17, Issue 4, 2004, Pages 473-477

  Liang, Jin ^a   Xiao, Ti Jun ^a   Van Casteren, J ^b  

^a UNIVERSITY OF SCIENCE AND TECHNOLOGY OF CHINA   (China)

^b UNIVERSITY OF ANTWERP   (Belgium)

Author keywords

Families of operators; Infinite delay; Mild solutions; Semilinear abstract functional differential equations; Semilinear abstract functional integrodifferential equations

Indexed keywords

BOUNDARY CONDITIONS; DIFFERENTIAL EQUATIONS; FUNCTIONS; INTEGRODIFFERENTIAL EQUATIONS; MATHEMATICAL OPERATORS; OPTIMIZATION; PROBLEM SOLVING;

INFINITE DELAY; MILD SOLUTIONS; SEMILINEAR ABSTRACT FUNCTIONAL DIFFERENTIAL EQUATIONS; SEMILINEAR FUNCTIONAL INTEGRODIFFERENTIAL EQUATIONS;

THEOREM PROVING;

EID: 1842790105     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0893-9659(04)90092-4     Document Type: Article

References (15)

1. J. Liang, F.L. Huang and T.J. Xiao, Exponential stability for abstract linear autonomous functional differential equations with infinite delay, Inter. J. Math. Math. Sci. 21, 255-260, (1998).
2. J. Liang and T.J. Xiao, Functional differential equations with infinite delay in Banach spaces, Inter. J. Math. and Math. Sci. 14, 497-508, (1991).
3. J. Liang and T.J. Xiao, Solutions of abstract functional differential equations with infinite delay, Acta Math. Sinica 34, 631-644, (1991).
4. J. Liang and T.J. Xiao, The Cauchy problem for nonlinear abstract functional differential equations with infinite delay, Computers Math. Applic. 40 (6/7), 693-703, (2000).
5. J.K. Hale and J. Kato, Phase space for retarded equations with infinite delay, Funkcialaj Ekvacioj 21, 11-41, (1978).
6. F.L. Huang, On linear autonomous functional differential equations with infinite delay, Ann. of Diff. Eqs. 3 (3), 275-292, (1987).
7. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, (1983).
8. O. Diekmann, S. van Gils, S. Lunel and H.O. Walther, Delay equations. Functional-, complex-, and nonlinear analysis, Appl. Math. Sci. 110, Springer-Verlag, Berlin, (1995).
9. K.-J. Engel and R. Nagel, One-parameter semigroups for linear evolution equations, GTM 194, Springer, Berlin, (2000).
10. J.A. Goldstein, Semigroups of Linear Operators and Applications, Oxford, New York, (1985).
11. R. Grimmer, Resolvent operators for integral equations in Banach space, Trans. Amer. Math. Soc. 273, 333-340, (1982).
12. J. Liang and T.J. Xiao, Functional differential equations with infinite delay in Fréchet spaces, J. Sichuan Univ. (Sichuan Daxue Xuebao) 26, 382-390, (1989).
13. R. deLaubenfels, Existence families, functional calculi and evolution equations, Lect. Notes in Math. 1570 Springer-Verlag, Berlin, (1994).
14. T.J. Xiao and J. Liang, The Cauchy problem for higher order abstract differential equations, Lect. Notes in Math. 1701, Springer, Berlin, (1998).
15. K. Schumacher, Existence and continuous dependence for functional differential equations with unbounded delay, Arch. Rat. Mech. Ana. 67, 315-335, (1978).