Almost automorphic mild solutions to some partial neutral functional-differential equations and applications

Nonlinear Analysis, Theory, Methods and Applications

Volumn 69, Issue 5-6, 2008, Pages 1485-1493

  Diagana, Toka ^a   Henriquez, Hernán R ^b   Hernández, Eduardo M ^b,c  

^a HOWARD UNIVERSITY   (United States)

^b UNIVERSIDAD DE SANTIAGO DE CHILE   (Chile)

^c UNIVERSITY OF SÃO PAULO   (Brazil)

Author keywords

Almost automorphic function; Compactly almost automorphic; Partial functional differential equations

Indexed keywords

BESSEL FUNCTIONS; BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; DIFFERENCE EQUATIONS; DIFFERENTIAL EQUATIONS; DIFFERENTIATION (CALCULUS); EXTRAPOLATION; INITIAL VALUE PROBLEMS; MATHEMATICAL MORPHOLOGY; NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS;

(SPM) CLASSES; BOUNDARY VALUES; ELSEVIER (CO); EXISTENCE AND UNIQUENESS; FIRST ORDERS; FUNCTIONAL DIFFERENTIAL EQUATIONS; IN CONTROL; MILD SOLUTIONS; SUFFICIENT CONDITIONS (SC);

CONTROL SYSTEMS;

EID: 44649086371     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2007.06.048     Document Type: Article

References (22)

1. Adimy M., and Ezzinbi K. Strict solutions of nonlinear hyperbolic neutral differential equations. Appl. Math. Lett. 12 1 (1999) 107-112
2. Bochner S. A new approach to almost periodicity. Proc. Natl. Acad. Sci. USA 48 (1962) 2039-2043
3. Diagana T., N'Guérékata G.M., and Minh N.V. Almost automorphic solutions of evolution equations. Proc. Amer. Math. Soc. 132 11 (2004) 3289-3298
4. Liu J., N'Guérékata G., and van Minh N. A Massera type theorem for almost automorphic solutions of differential equations. J. Math. Anal. Appl. 299 2 (2004) 587-599
5. Hale J.K., and Verduyn Lunel S.M. Introduction to Functional-Differential Equations. Applied Mathematical Sciences vol. 99 (1993), Springer-Verlag, New York
6. Hale J.K. Partial neutral functional-differential equations. Rev. Roumaine Math. Pures Appl. 39 4 (1994) 339-344
7. Hernández E., and Henríquez H.R. Existence results for partial neutral functional differential equations with unbounded delay. J. Math. Anal. Appl. 221 2 (1998) 452-475
8. Hernández E., and Henríquez H.R. Existence of periodic solutions of partial neutral functional differential equations with unbounded delay. J. Math. Anal. Appl. 221 2 (1998) 499-522
9. Hernández E. Existence results for partial neutral integrodifferential equations with unbounded delay. J. Math. Anal. Appl. 292 1 (2004) 194-210
10. Hernández E.M., and Pelicer M.L. Asymptotically almost periodic and almost periodic solutions for partial neutral differential equations. Appl. Math. Lett. 18 11 (2005) 1265-1272
11. Hino Y., and Murakami S. Almost automorphic solutions for abstract functional differential equations. J. Math. Anal. Appl. 286 (2003) 741-752
12. Hino Y., Murakami S., and Naito T. Functional-Differential Equations with Infinite Delay. Lecture Notes in Mathematics vol. 1473 (1991), Springer-Verlag, Berlin
13. Minh Man N., and Van Minh N. On the existence of quasi periodic and almost periodic solutions of neutral functional differential equations. Commun. Pure Appl. Anal. 3 2 (2004) 291-300
14. N'Guérékata G.M. Almost Automorphic Functions and Almost Periodic Functions in Abstract Spaces (2001), Kluwer Academic/Plenum Publishers, New York, London, Moscow
15. N'Guérékata G.M. Topics in Almost Automorphy (2005), Springer, New York, Boston, Dordrecht, London, Moscow
16. Yuan R. Existence of almost periodic solutions of neutral functional-differential equations via Liapunov-Razumikhin function. Z. Angew. Math. Phys. 49 1 (1998) 113-136
17. Wu J., and Xia H. Rotating waves in neutral partial functional-differential equations. J. Dynam. Differential Equations 11 2 (1999) 209-238
18. Wu J., and Xia H. Self-sustained oscillations in a ring array of coupled lossless transmission lines. J. Differential Equations 124 1 (1996) 247-278
19. Wu J. Theory and Applications of Partial Functional-Differential Equations. Applied Mathematical Sciences vol. 119 (1996), Springer-Verlag, New York
20. Veech W.A. Almost automorphic functions. Proc. Natl. Acad. Sci. USA 49 (1963) 462-464
21. Zaidman S. Almost automorphic solutions of some abstract evolution equations. II. Istit. Lombardo Accad. Sci. Lett. Rend. A 111 2 (1977) 260-272
22. Zaki M. Almost automorphic solutions of certain abstract differential equations. Ann. Mat. Pura Appl. 101 4 (1974) 91-114