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http://dx.doi.org/10.4134/CKMS.c200370

BOUNDED AND PERIODIC SOLUTIONS OF INHOMOGENEOUS LINEAR EVOLUTION EQUATIONS  

Duoc, Trinh Viet (Faculty of Mathematics, Mechanics, and Informatics VNU University of Science and Thang Long Institute of Mathematics and Applied Sciences)
Publication Information
Communications of the Korean Mathematical Society / v.36, no.4, 2021 , pp. 759-770 More about this Journal
Abstract
The purpose of this paper is to prove unique existence of bounded solution and periodic solution to inhomogeneous linear evolution equations which trajectories of these solutions belong to given admissible Banach function space.
Keywords
Exponential dichotomy; admissible Banach function spaces; evolution family; bounded and periodic solutions; inhomogeneous linear evolution equations;
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1 S. Boulaaras and N. Doudi, Global existence and exponential stability of coupled Lame system with distributed delay and source term without memory term, Bound. Value Probl. 2020 (2020), Paper No. 173, 21 pp. https://doi.org/10.1186/s13661-020-01471-9   DOI
2 A. Choucha, S. Boulaaras, and D. Ouchenane, Exponential decay of solutions for a viscoelastic coupled Lame system with logarithmic source and distributed delay terms, Math. Methods Appl. Sci. 44 (2021), no. 6, 4858-4880. https://doi.org/10.1002/mma.7073   DOI
3 Ju. L. Daleckii and M. G. Krein, Stability of solutions of differential equations in Banach space, translated from the Russian by S. Smith, Translations of Mathematical Monographs, Vol. 43, American Mathematical Society, Providence, RI, 1974.
4 J. L. Massera and J. J. Schaffer, Linear Eifferential Equations and Function Spaces, Pure and Applied Mathematics, Vol. 21, Academic Press, New York, 1966.
5 A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Applied Mathematical Sciences, 44, Springer-Verlag, New York, 1983. https://doi.org/10.1007/978-1-4612-5561-1   DOI
6 J. Kato, T. Naito, and J. S. Shin, Bounded solutions and periodic solutions to linear differential equations in Banach spaces, Vietnam J. Math. 30 (2002), suppl., 561-575.
7 A. Beniani, N. Taouaf, and A. Benaissa, Well-posedness and exponential stability for coupled Lame system with viscoelastic term and strong damping, Comput. Math. Appl. 75 (2018), no. 12, 4397-4404. https://doi.org/10.1016/j.camwa.2018.03.037   DOI
8 N. T. Huy, Exponential dichotomy of evolution equations and admissibility of function spaces on a half-line, J. Funct. Anal. 235 (2006), no. 1, 330-354. https://doi.org/10.1016/j.jfa.2005.11.002   DOI
9 K.-J. Engel and R. Nagel, One-parameter Semigroups for Linear Evolution Equations, Graduate Texts in Mathematics, 194, Springer-Verlag, New York, 2000.
10 R. Nagel and G. Nickel, Well-posedness for nonautonomous abstract Cauchy problems, in Evolution equations, semigroups and functional analysis (Milano, 2000), 279-293, Progr. Nonlinear Differential Equations Appl., 50, Birkhauser, Basel, 2002.
11 A. Choucha, S. Boulaaras, D. Ouchenane, and S. Beloul, General decay of nonlinear viscoelastic Kirchhoff equation with Balakrishnan-Taylor damping, logarithmic nonlinearity and distributed delay terms, Math. Methods Appl. Sci. 44 (2021), no. 7, 5436-5457. https://doi.org/10.1002/mma.7121   DOI
12 N. V. Minh, F. Rabiger, and R. Schnaubelt, Exponential stability, exponential expansiveness, and exponential dichotomy of evolution equations on the half-line, Integral Equations Operator Theory 32 (1998), no. 3, 332-353. https://doi.org/10.1007/BF01203774   DOI