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Composition of pseudo almost-periodic functions and semilinear differential equations. (English) Zbl 1047.47030

The authors give an abstract result on the composition of pseudo almost-periodic functions as introduced by C. Zhang [J. Math. Anal. Appl. 181, 62–76 (1994; Zbl 0796.34029)]. They apply this result to obtain pseudo almost-periodic solutions to semilinear abstract Cauchy problems.

MSC:

47D06 One-parameter semigroups and linear evolution equations
34G20 Nonlinear differential equations in abstract spaces
47G99 Integral, integro-differential, and pseudodifferential operators

Citations:

Zbl 0796.34029
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Full Text: DOI

References:

[1] Dads, E. Ait; Arino, O., Exponential dichotomy and existence of pseudo almost-periodic solutions for some differential equations, Nonlinear Anal., 27, 369-386 (1996) · Zbl 0855.34055
[2] Dads, E. Ait; Ezzinbi, K.; Arino, O., Pseudo almost-periodic solutions for some differential equations, Nonlinear Anal., 28, 1141-1155 (1997) · Zbl 0874.34041
[3] Amir, B.; Maniar, L., Composition of pseudo almost-periodic functions and semilinear Cauchy problem with nondense domain, Tübinger Ber. Funktionalanal. Heft 6 Jahrgang, 6-16 (96/97) · Zbl 0941.34059
[4] Fink, A. M., Almost Periodic Differential Equations. Almost Periodic Differential Equations, Lecture Notes in Math., 377 (1974), Springer-Verlag: Springer-Verlag New York/Berlin · Zbl 0325.34039
[5] Pazy, A., Semi Group of Linear Operators and Applications to Partial Differential Equations (1983), Springer-Verlag: Springer-Verlag New York · Zbl 0516.47023
[6] C. Zhang, Pseudo Almost-Periodic Functions and Their Applications, thesis, The University of Western Ontario, 1992.; C. Zhang, Pseudo Almost-Periodic Functions and Their Applications, thesis, The University of Western Ontario, 1992.
[7] Zhang, C., Pseudo almost-periodic solutions of some differential equations, J. Math. Anal. Appl., 181, 62-76 (1994) · Zbl 0796.34029
[8] Zhang, C., Pseudo almost-periodic solutions of some differential equations II, J. Math. Anal. Appl., 192, 543-561 (1995) · Zbl 0826.34040
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