Existence results for partial neutral integro-differential equation with unbounded delay

Applicable Analysis

Volumn 86, Issue 2, 2007, Pages 223-237

  Hernández M, Eduardo ^a   Dos Santos, José P C ^a  

^a UNIVERSITY OF SÃO PAULO   (Brazil)

Author keywords

2000 Mathematics Subject Classifications: 47D09; 34G10; 47N20; Abstract Cauchy problem; Resolvents operators

Indexed keywords

EID: 64849111140     PISSN: 00036811     EISSN: 1563504X     Source Type: Journal    
DOI: 10.1080/00036810601148216     Document Type: Article

References (19)

1. Cannarsa, P, and Sforza, D. 2003. Global solutions of abstract semilinear parabolic equations with memory terms. NoDEA Nonlinear Differential Equations and Applications, 10 (4): 399–430.
2. Clément, P, and Nohel, JA. 1981. Asymptotic behavior of solutions of nonlinear Volterra equations with completely positive kernels. SIAM Journal on Mathematical Analysis, 12 (4): 514–535.
3. Clément, P, and Prüss, J. 1992. Global existence for a semilinear parabolic Volterra equation. Mathematische Zeitschrift, 209 (1): 17–26.
4. Granas, A, and Dugundji, J. 2003. “ Fixed Point Theory ”. New York: Springer-Verlag.
5. Grimmer, RC, and Kappel, F. 1984. Series expansions for resolvents of Volterra integro-differential equations in Banach space. SIAM Journal on Mathematical Analysis, 15 (3): 595–604.
6. Grimmer, R, and Prüss, J. 1985. On linear Volterra equations in Banach spaces. Hyperbolic partial differential equations, II. Computers & Mathematics with Applications, 11 (1–3): 189–205.
7. Gurtin, ME, and Pipkin, AC. 1968. A general theory of heat conduction with finite wave speed. Archive for Rational Mechanics and Analysis, 31: 113–126.
8. Hale, JK, and Verduyn Lunel, SM. 1993. “ Applied Mathematical Sciences ”. In Introduction to Functional-Differential Equations, Vol. 99, New York: Springer-Verlag.
9. Hale, JK. 1994. Partial neutral functional-differential equations. Revue Roumaine de Mathematiques Pures et Appliquees (Romanian Journal of Pure and Applied Mathematics), 39 (4): 339–344.
10. Hernández, E, and Henríquez, HR. 1998. Existence results for partial neutral functional differential equations with unbounded delay. Journal of Mathematics Analysis and Applications, 221 (2): 452–475.
11. Hernández, E. 2004. Existence results for partial neutral integrodifferential equations with unbounded delay. Journal of Mathematics Analysis and Applications, 292 (1): 194–210.
12. Hernández, E, and McKibben, M. 2005. Some comments on: “Existence of solutions of abstract nonlinear second-order neutral functional integrodifferential equations”. Computers & Mathematics with Applications, 50 (5–6): 655–669.
13. Henríquez, HR. 1997. Regularity of solutions of abstract retarded functional-differential equations with unbounded delay. Nonlinear Analysis, 28 (3): 513–531.
14. Hino, Y, Murakami, S, and Naito, T. 1991. “ Lecture Notes in Mathematics ”. In Functional-differential equations with infinite delay, Vol. 1473, Berlin: Springer-Verlag.
15. Lunardi, A. 1990. On the linear heat equation with fading memory. SIAM Journal on Mathematical analysis, 21 (5): 1213–1224.
16. Martin, RH. 1987. Nonlinear Operators and Differential Equations in Banach Spaces, Floride: Robert E. Krieger Publ. Co.
17. Nunziato, JW. 1971. On heat conduction in materials with memory,. Quarterly of Applied Mathematics, 29: 187–204.
18. Wu, J, and Xia, H. 1999. Rotating waves in neutral partial functional-differential equations. Journal of Dynamics and Differential Equations, 11 (2): 209–238.
19. Wu, J. 1996. “ Applied Mathematical Sciences ”. In Theory and applications of partial functional-differential equations., Vol. 119, New York: Springer-Verlag.