Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-18T15:05:37.290Z Has data issue: false hasContentIssue false
  • English
  • Français

WEIGHTED PSEUDO-ALMOST PERIODIC SOLUTIONS FOR SOME ABSTRACT DIFFERENTIAL EQUATIONS WITH UNIFORM CONTINUITY

Part of: Qualitative theory Harmonic analysis in one variable

Published online by Cambridge University Press:  13 October 2010

LI-LI ZHANG  and
HONG-XU LI
LI-LI ZHANG
Affiliation:
Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, PR China (email: [email protected])
HONG-XU LI*
Affiliation:
Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, PR China (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this work, we give some theorems on (mild) weighted pseudo-almost periodic solutions for some abstract semilinear differential equations with uniform continuity. To facilitate this we give a new composition theorem of weighted pseudo-almost periodic functions. Our composition theorem improves the known one by making use of a uniform continuity condition instead of the Lipschitz condition.

Keywords

almost periodicweighted pseudo-almost periodicuniform continuityfixed pointC0-semigroup

MSC classification

Secondary: 34C27: Almost and pseudo-almost periodic solutions 42A75: Classical almost periodic functions, mean periodic functions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 82 , Issue 3 , December 2010 , pp. 424 - 436
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

References

[1]Ait Dads, E. and Arino, O., ‘Exponential dichotomy and existence of pseudo almost-periodic solutions for some differential equations’, Nonlinear Anal. 27 (1996), 369–386.CrossRefGoogle Scholar
[2]Ait Dads, E., Cieutat, P. and Ezzinbi, K., ‘The existence of pseudo almost-periodic solutions for some nonlinear differential equations in Banach spaces’, Nonlinear Anal. 69 (2008), 1325–1342.CrossRefGoogle Scholar
[3]Ait Dads, E., Ezzinbi, K. and Arino, O., ‘Pseudo almost-periodic solutions for some differential equations’, Nonlinear Anal. 28 (1997), 1141–1155.CrossRefGoogle Scholar
[4]Amir, B. and Maniar, L., ‘Composition of pseudo almost-periodic functions and Cauchy problems with operator of nondense domain’, Ann. Math. Blaise Pascal 6 (1999), 1–11.CrossRefGoogle Scholar
[5]Corduneanu, C., Almost Periodic Functions, 2nd edn (Chelsea, New York, 1989).Google Scholar
[6]Cuevas, C. and Lizama, C., ‘Almost automorphic solutions to a class of semilinear fractional differential equations’, Appl. Math. Lett. 21 (2008), 1315–1319.CrossRefGoogle Scholar
[7]Cuevas, C. and Pinto, M., ‘Existence and uniqueness of pseudo-almost periodic solutions of semilinear Cauchy problem with non dense domain’, Nonlinear Anal. 45 (2001), 73–83.CrossRefGoogle Scholar
[8]Diagana, T., ‘Weighted pseudo almost periodic functions and applications’, C. R. Acad. Sci. Paris, Ser. I 343 (2006), 643–646.CrossRefGoogle Scholar
[9]Diagana, T., ‘Existence and uniqueness of pseudo almost periodic solutions to some classes of partial evolution equations’, Nonlinear Anal. 66 (2007), 384–395.CrossRefGoogle Scholar
[10]Diagana, T., ‘Weighted pseudo-almost periodic solutions to some differential equations’, Nonlinear Anal. 68 (2008), 2250–2260.CrossRefGoogle Scholar
[11]Fink, A. M., Almost Periodic Differential Equations, Lecture Notes in Mathematics, 377 (Springer, New York, 1974).CrossRefGoogle Scholar
[12]Li, H. X., Huang, F. L. and Li, J. Y., ‘Composition of pseudo almost-periodic functions and semilinear differential equations’, J. Math. Anal. Appl. 255 (2001), 436–446.CrossRefGoogle Scholar
[13]N’Guérékata, G. M., Almost Automorphic Functions and Almost Periodic Functions in Abstract Spaces (Kluwer Academic/Plenum Publishers, New York, London, Moscow, 2001).CrossRefGoogle Scholar
[14]Zhang, C. Y., ‘Pseudo almost periodic solutions of some differential equations’, J. Math. Anal. Appl. 181 (1994), 62–76.CrossRefGoogle Scholar
[15]Zhang, C. Y., ‘Integration of vector-valued pseudo almost periodic functions’, Proc. Amer. Math. Soc. 121 (1994), 167–174.CrossRefGoogle Scholar
[16]Zhang, C. Y., ‘Pseudo almost periodic solutions of some differential equations, II’, J. Math. Anal. Appl. 192 (1995), 543–561.CrossRefGoogle Scholar