Perturbation theory of abstract Cauchy problems and Volterra equations

Nonlinear Analysis, Theory, Methods and Applications

Volumn 30, Issue 6, 1997, Pages 3521-3528

  Chang, Jung Chan ^a   Shaw, Sen Yen ^a  

^a NATIONAL CENTRAL UNIVERSITY   (Taiwan)

Author keywords

Abstract Cauchy problem; Additive perturbation; C0 semigroup; Cosine operator function; Multiplicative perturbation; Resolvent family; Volterra equation

Indexed keywords

EID: 0000544284     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(97)00054-0     Document Type: Article

References (17)

1. Arendt W. and Kellermann H., Integrated solutions of Volterra integro-differential equations and applications, in Proceedings of the Conference on Volterra Integrodifferential Equations in Banach Spaces and Applications, Trento 1987, Pitman Research Notes Math. Ser., vol.190, Longman Sci. Tech., Harlow, 1989
2. Chang J.-C. and Shaw S.-Y., Rates of approximation and ergodic limits of resolvent families, Arch. Math. 66, 320-330 (1996).
3. Chang J.-C. and Shaw S.-Y., Multiplicative and additive perturbations of resolvent families, preprint (1996).
4. Da Prato G. and Iannelli M., Linear integro-differential equation in Banach space Rend. Sem. Math. Padova 62, 207-219 (1980).
5. Desch W. and Schappacher W., Some generation results for perturbed semigroups, in Trends in Semigroup Theory and Application, Ph. Clement et al (Eds.), Marcel Dekker, New york, 1989, pp. 125-152.
6. Fattorini H. O., Ordinary differential equations in linear topological spaces, I, J. Differential Eq. 5, 72-105 (1968).
7. Goldstein J., Semigroups of Linear Operators and Applications, Oxford, 1985.
8. Gustafson K. and Lumer G., Multiplicative perturbation of semigroup generators, Pacific J. Math. 41, 731-742 (1972).
9. Miyadera I., A perturbation theory for semigroups of operators, Tohoku Math. J. 18, 299-310 (1966).
10. 0-semigroups and some applications to step responses and cumulative outputs, J. Funct. Anal. 128, 315-340 (1995).
11. Piskarev S. and Shaw S.-Y., Perturbation and comparison of cosine functions, Semigroup Forum 51, 225-246 (1995).
12. Prüss J., Positivity and regularity of Volterra equation in Banach space, Math. Ann. 279, 317-347 (1987).
13. Prüss J., Evolutionary Integral Equations and Applications, Monographs in Mathematics Vol. 87, Birkhaüser Verlag, 1993.
14. Rhandi A., Positive perturbations of Volterra linear equations and sine functions of operators, J. Integral Equations Appl. 4, 409-420 (1994).
15. Rhandi A., Multiplicative perturbations of linear Volterra equations, Proc. Amer. Math. Soc. 119, 493-501 (1993).
16. Serizawa H. and Watanabe M., Perturbation for cosine families on Banach spaces, Houston J. Math. 12, 117-124 (1986).
17. Shimizu M. and Miyadera I., Perturbation theory for cosine families on Banach spaces, Tokyo J. Math. 1, 333-343 (1978).