Almost periodic linear differential equations with non-separated solutions

Journal of Functional Analysis

Volumn 237, Issue 2, 2006, Pages 402-426

  Ortega, Rafael ^a   Tarallo, Massimo ^b  

^a UNIVERSITY OF GRANADA   (Spain)

^b Dipartimento di Matematica dell'Universita   (Italy)

Author keywords

Almost periodic solutions; Favard's theory; Homoclinic solutions

Indexed keywords

EID: 33646918615     PISSN: 00221236     EISSN: 10960783     Source Type: Journal    
DOI: 10.1016/j.jfa.2006.03.027     Document Type: Article

References (17)

1. Besicovitch A.S. Almost Periodic Functions (1954), Dover
2. Cieutat P., and Haraux A. Exponential decay existence of almost periodic solutions for some linear forced differential equations. Port. Math. (N.S.) 59 (2002) 141-159
3. Conley C.C., and Miller R.K. Asymptotic stability without uniform stability: Almost periodic coefficients. J. Differential Equations 1 (1965) 333-336
4. Demenchuk A.K. Quasiperiodic solutions of linear nonhomogeneous differential equations. Differ. Equ. 37 (2001) 763-767
5. Favard J. Sur les equations différentielles linéaires à coefficients presque-périodiques. Acta Math. 51 (1927) 31-81
6. Favard J. Sur certains systèmes différentielles scalaires linéaires et homogènes à coefficients presque-périodiques. Ann. Mat. Pura Appl. 61 (1963) 297-316
7. Fink A.M. Almost Periodic Differential Equations. Lecture Notes in Math. vol. 377 (1974), Springer-Verlag
8. Haraux A. Systèmes dynamiques dissipatifs et applications (1991), Masson
9. Johnson R.A. A linear almost periodic equation with an almost automorphic solution. Proc. Amer. Math. Soc. 82 (1981) 199-205
10. Levitan B.M., and Zhikov V.V. Almost Periodic Functions and Differential Equations (1982), Cambridge Univ. Press
11. Moshchevitin N.G. Recurrence of the integral of a smooth conditionally periodic function. Math. Notes 63 (1998) 648-657
12. Nakajima F. Separation conditions and stability properties in almost periodic systems. Tohoku Math. J. 26 (1974) 305-314
13. Nemytskii V.V., and Stepanov V.V. Qualitative Theory of Differential Equations (1960), Princeton Univ. Press
14. Palmer K.J. On bounded solutions of almost periodic linear differential systems. J. Math. Anal. Appl. 103 (1984) 16-25
15. Pontryagin L.S. Topological Groups (1966), Gordon & Breach
16. Yoshizawa T. Favard's condition in linear almost periodic systems. In: Antosiewicz H.A. (Ed). International Conference on Differential Equations (1975), Academic Press 787-799
17. Zhikov V.V., and Levitan B.M. Favard theory. Russian Math. Surveys 32 (1977) 129-180