Existence of solutions for second order partial neutral functional differential equations

Integral Equations and Operator Theory

Volumn 62, Issue 2, 2008, Pages 191-217

  Morales, Eduardo Hernández ^a   Henríquez, Hernán R ^b   McKibben, Mark A ^c  

^a UNIVERSITY OF SÃO PAULO   (Brazil)

^b UNIVERSIDAD DE SANTIAGO DE CHILE   (Chile)

^c GOUCHER COLLEGE   (United States)

Author keywords

Cosine function of operators; Neutral partial differential equations

Indexed keywords

EID: 53849088241     PISSN: 0378620X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00020-008-1618-1     Document Type: Article

References (27)

1. M. Adimy, K. Ezzinbi and M. Laklach, Existence of solutions for a class of partial neutral differential equations. C. R. Acad. Sci. Paris Sir. I Math. 330 (11) (2000), 957-962.
2. M. Adimy, H. Bouzahir and K. Ezzinbi, Existence and stability for some partial neutral functional differential equations with infinite delay, J. Math. Anal. Appl. 294 (2) (2004), 438-461.
3. M. Adimy and K. Ezzinbi, A class of linear partial neutral functional-differential equations with nondense domain. J. Diff. Eqns. 147 (2) (1998), 285-332.
4. W. Arendt, C.J.K. Batty, M. Hieber and F. Neubrander, Vector-valued Laplace Transforms and Cauchy Problems, Birkhäuser Verlag, Basel, 2001.
5. K. Balachandran, D.G. Park and S.M. Anthoni, Existence of solutions of abstractnonlinear second-order neutral functional integrodifferential equations. Comput. Math. Appl. 46 (8-9) (2003), 1313-1324.
6. M. Benchohra, J. Henderson and S.K. Ntouyas, Existence results for impulsive multivalued semilinear neutral functional differential inclusions in Banach spaces. J. Math. Anal. Appl. 263 (2) (2001), 763-780.
7. M. Benchohra, E. Gatsori and S.K. Ntouyas, Multivalued semilinear neutral functional differential equations with nonconvex-valued right-hand side. Abstr. Appl. Anal. 2004, no. 6, 525-541.
8. T.A. Burton and C. Kirk, A fixed point theorem of Krasnoselskii-Schaefer type. Math. Nachr. 189 (1998), 23-31.
9. H.O. Fattorini, Second Order Linear Differential Equations in Banach Spaces, North-Holland Mathematics Studies, Vol. 108, North-Holland, Amsterdam, 1985.
10. A. Granas and J. Dugundji, Fixed Point Theory. Springer-Verlag, New York, 2003.
11. J.K. Hale, Partial neutral functional-differential equations. Rev. Roumaine Math Pures Appl. 39 (4) (1994), 339-344.
12. J.K. Hale and S.M. Verduyn Lunel, Introduction to Functional-Differential Equations. Applied Mathematical Sciences, 99. Springer-Verlag, New York, 1993.
13. E. Hernández and C.H. Vásquez, Differentiability of solutions of second-order functional differential equations with unbounded delay. J. Math. Anal. Appl. 280 (2003), 284-312.
14. E. Hernández and H.R. Henŕquez, Existence of periodic solutions of partial neutral functional-differential equations with unbounded delay. J. Math. Anal. Appl. 221 (2) (1998), 499-522.
15. E. Hernández and H.R. Henr?́quez, Existence results for partial neutral functionaldifferential equations with unbounded delay. J. Math. Anal. Appl. 221 (2) (1998), 452-475.
16. E. Hernández, Existence results for partial neutral integrodifferential equations with unbounded delay. J. Math. Anal. Appl. 292 (1) (2004), 194-210.
17. E. Hernandez and M.A. McKibben, M. A., "Some comments on: Existence of solutions of abstract nonlinear second-order neutral functional integrodifferential equations, in Comput. Math. Appl. 46 (8-9) (2003)". Comput. Math. Appl. 50 (5-6) (2005), 655-669.
18. Y. Hino, S. Murakami and T. Naito, Functional-Differential Equations with Infinite Delay. Lecture Notes in Mathematics, 1473. Springer-Verlag, Berlin, 1991.
19. J. Kisyński, On cosine operator functions and one parameter group of operators, Studia Math. 49 (1972), 93-105.
20. V. Kolmanovskii and A. Myshkis, Introduction to the Theory and Applications of Functional Differential Equations. Kluwer Acad. Publ., Dordrecht, 1999.
21. V. Lakshmikantham, L. Wen and B. Zhang, Theory of Differential Equations with Unbounded Delay. Kluwer Acad. Publ., Dordrecht, 1994.
22. H.J. Lee, J. Park and J.Y. Park, Existence results for second-order neutral functional differential and integrodifferential inclusions in Banach spaces. Electron. J. Differential Equations 96 (2002), 13 pp. (electronic).
23. R.H. Martin, Nonlinear Operators and Differential Equations in Banach Spaces, Robert E. Krieger Publ. Co., Florida, 1987.
24. C.C. Travis and G.F. Webb, Cosine families and abstract nonlinear second order differential equations. Acta Math. Acad. Sci. Hungaricae, 32 (1978), 76-96.
25. C.C. Travis and G.F. Webb, Compactness, regularity, and uniform continuity properties of strongly continuous cosine families, Houston J. Math. 3 (4) (1977) 555-567.
26. J. Wu and H. Xia, Rotating waves in neutral partial functional- differential equations. J. Dynam. Diff. Eqns. 11 (2) (1999), 209-238.
27. J. Wu and H. Xia, Self-sustained oscillations in a ring array of coupled lossless transmission lines. J. Diff. Eqns. 124 (1) (1996), 247-278.