Bohr-Neugebauer type theorem for some partial neutral functional differential equations

Nonlinear Analysis, Theory, Methods and Applications

Volumn 66, Issue 5, 2007, Pages 1145-1160

  Adimy, Mostafa ^a   Elazzouzi, Abdelhai ^b   Ezzinbi, Khalil ^b  

^a UNIVERSITÉ DE PAU ET DES PAYS DE L'ADOUR   (France)

^b FACULTÉ DES SCIENCES SEMLALIA   (Morocco)

Author keywords

Almost periodic solution; Essential growth; Hille Yosida condition; Neutral equation; Semigroup; Spectral decomposition; Variation of constants formula

Indexed keywords

DECOMPOSITION; NUMERICAL METHODS; PROBLEM SOLVING; THEOREM PROVING;

ALMOST PERIODIC SOLUTION; CONSTANTS FORMULA; HILLE-YOSIDA CONDITION; NEUTRAL EQUATION; PARTIAL NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS; SEMIGROUP; SPECTRAL DECOMPOSITION;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 33845362045     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2006.01.011     Document Type: Article

References (26)

1. Adimy M., and Ezzinbi K. Equation de type neutre et semi groupes intégrés. Comptes Rendus Académie des Sciences Paris t. 318 Série I (1994) 529-534
2. Adimy M., and Ezzinbi K. A class of linear partial neutral functional differential equations with non-dense domain. Journal of Differential Equations 147 2 (1998) 285-332
3. Adimy M., and Ezzinbi K. Strict solutions of nonlinear hyperbolic neutral differential equations. Applied Mathematics Letters 12 (1999) 107-112
4. Adimy M., and Ezzinbi K. Existence and linearized stability for partial neutral functional differential equations. Differential Equations and Dynamical Systems 7 (1999) 371-417
5. Adimy M., and Ezzinbi K. Existence and stability of solutions for a class of partial neutral functional differential equations. Hiroshima Mathematical Journal 34 3 (2004) 251-294
6. Adimy M., Ezzinbi K., and Laklach M. Spectral decomposition for partial neutral functional differential equations. Canadian Applied Mathematics Quarterly 9 1 (2001) 1-34
7. Arendt W., Batty C.J.K., Hieber M., and Neubrander F. Vector-Valued Laplace Transforms and Cauchy Problems. Monographs in Mathematics vol. 96 (2001), Birkhäuser Verlag
8. Benkhalti R., and Ezzinbi K. A Massera type criterion for some partial functional differential equations. Dynamic Systems and Application 9 2 (2000) 221-228
9. Benkhalti R., Bouzahir H., and Ezzinbi K. Existence of a periodic solution for some partial functional differential equations with infinite delay. Journal of Mathematical Analysis and Applications 256 1 (2001) 257-280
10. Da Prato G., and Sinestrari E. Differential operators with non dense domain. Annali Scuola Normale Superiore di Pisa 14 2 (1987) 285-344
11. Engel K.-J., and Nagel R. One-Parameter Semigroups of Linear Evolution Equations. Graduate Texts in Mathematics vol. 194 (2000), Springer-Verlag
12. Ezzinbi K., and Liu J.H. Periodic solutions of non-densely defined delay evolution equations. Journal of applied Mathematics and Stochastic Analysis 15 2 (2002) 113-123
13. Fink A. Almost Periodic Differential Equations. Lectures Notes vol. 377 (1974), Springer-Verlag
14. Furumouchi T., Naito T., and Minh N.V. Boundedness and almost periodicity of solutions of partial functional differential equations. Journal of Differential Equations 180 1 (2002) 125-152
15. Hale J.K., and Verduyn-Lunel S.M. Introduction to Functional Differential Equations. Applied Mathematical Sciences vol. 99 (1993), Springer-Verlag
16. Hale J.K. Partial neutral functional differential equations. Revue Roumaine de Mathématiques Pures et Appliquées 39 4 (1994) 339-344
17. Hale J.K. Coupled oscillators on a circle. Resenhas do Instituto de Matemática e Estatística da Universidade de São Paulo 1 4 (1994) 441-457
18. Hino Y., and Murakami S. Existence of an almost periodic solution of abstract linear functional differential equations with infinite delay. Dynamic Systems and Applications 5 3 (1996) 385-399
19. Massera J.L. The existence of periodic solutions of systems of differential equations. Duke Mathematical Journal 17 (1950) 457-475
20. Murakami S., Naito T., and Minh N.V. Massera Theorem for almost periodic solutions of functional differential equations. Journal of Mathematical Society of Japan 56 (2004) 247-268
21. Travis C.C., and Webb G.F. Existence and stability for partial functional differential equations. Transactions of the American Mathematical Society 200 (1974) 395-418
22. Zeidler E. Nonlinear Functional Analysis and its Applications, Tome I, Fixed Point Theorems (1993), Springer-Verlag
23. Webb G.F. Asymptotic stability for abstract nonlinear functional differential equations. Proceeding of the American Mathematical Society 54 (1976) 225-230
24. Wu J. Theory and Applications of Partial Functional Differential Equations vol. 119 (1996), Springer-Verlag
25. Wu J., and Xia H. Self-sustained oscillations in a ring array of coupled lossless transmission lines. Journal of Differential Equations 124 1 (1996) 247-278
26. Wu J., and Xia H. Rotating waves in neutral partial functional differential equations. Journal of Dynamics and Differential Equations 11 2 (1999) 209-238