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WEIGHTED PSEUDO ALMOST PERIODIC SOLUTIONS FOR DIFFERENTIAL EQUATIONS WITH PIECEWISE CONSTANT ARGUMENTS

Part of: Functional-differential and differential-difference equations

Published online by Cambridge University Press:  16 June 2015

LI-LI ZHANG  and
HONG-XU LI
LI-LI ZHANG*
Affiliation:
Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang, Hebei 050043, PR China email zllyou0@gmail.com
HONG-XU LI
Affiliation:
Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, PR China email hoxuli@sohu.com
*
✉zllyou0@gmail.com
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Abstract

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By applying the theory of exponential dichotomies and contraction mapping, we establish some existence and uniqueness results for weighted pseudo almost periodic solutions of some differential equations with piecewise constant arguments. For this purpose, we also describe some basic properties of weighted pseudo almost periodic sequences.

Keywords

exponential dichotomyweighted pseudo almost periodic sequenceweighted pseudo almost periodic solutionpiecewise constant argument

MSC classification

Primary: 34K14: Almost and pseudo-periodic solutions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 92 , Issue 2 , October 2015 , pp. 238 - 250
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

References

Ait Dads, E. and Lhachimi, L., ‘Pseudo almost periodic solutions for equation with piecewise constant argument’, J. Math. Anal. Appl. 371 (2010), 842–854.CrossRefGoogle Scholar
Alonso, A. I., Hong, J. L. and Obaya, R., ‘Exponential dichotomy and trichotomy for difference equations’, Comput. Math. Appl. 38 (1999), 41–49.CrossRefGoogle Scholar
Diagana, T., ‘Weighted pseudo almost periodic functions and applications’, C. R. Acad. Sci. Paris I 343 (2006), 643–646.CrossRefGoogle Scholar
Diagana, T., ‘Weighted pseudo-almost periodic solutions to some differential equations’, Nonlinear Anal. 68 (2008), 2250–2260.CrossRefGoogle Scholar
Fink, A. M., Almost Periodic Differential Equations, Lecture Notes in Mathematics, 377 (Springer, Berlin, 1974).CrossRefGoogle Scholar
Küpper, T. and Yuan, R., ‘On quasi-periodic solutions of differential equations with piecewise constant argument’, J. Math. Anal. Appl. 267 (2002), 173–193.CrossRefGoogle Scholar
Li, H. X., ‘Pseudo almost periodic sequences and some nonlinear differential equations with piecewise constant argument’, Nonlinear Funct. Anal. Appl. 10 (2005), 479–493.Google Scholar
Liang, J., Xiao, T. J. and Zhang, J., ‘Decomposition of weighted pseudo-almost periodic functions’, Nonlinear Anal. 73 (2010), 3456–3461.CrossRefGoogle Scholar
Palmer, K. J., ‘Exponential dichotomies, the shadowing lemma and transversal homoclinic points’, Dynam. Rep. 1 (1988), 265–306.CrossRefGoogle Scholar
Yuan, R., ‘The existence of almost periodic solutions of retarded differential equations with piecewise constant argument’, Nonlinear Anal. 48 (2002), 1013–1032.CrossRefGoogle Scholar
Yuan, R. and Hong, J. L., ‘The existence of almost periodic solutions for a class of differential equations with piecewise constant argument’, Nonlinear Anal. 28 (1997), 1439–1450.Google Scholar
Zhang, C. Y., ‘Pseudo almost periodic solutions of some differential equations’, J. Math. Anal. Appl. 181 (1994), 62–76.CrossRefGoogle Scholar
Zhang, L. L. and Li, H. X., ‘Weighted pseudo almost periodic solutions of second order neutral differential equations with piecewise constant argument’, Nonlinear Anal. 74 (2011), 6770–6780.CrossRefGoogle Scholar
Zhang, L. L. and Li, H. X., ‘Weighted pseudo almost periodic solutions of second-order neutral-delay differential equations with piecewise constant argument’, Comput. Math. Appl. 62 (2011), 4362–4376.CrossRefGoogle Scholar