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Bounded and periodic solutions of inhomogeneous linear evolution equations

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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.

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.

참고문헌 (12)

  1. Abderrahmane Beniani, "Well-posedness and exponential stability for coupled Lamé system with viscoelastic term and strong damping", Computers & Mathematics with Applications, 75(12), pp.4397~4404 (2018), Elsevier BV[DOI]
  2. Salah Boulaaras, "Global existence and exponential stability of coupled Lamé system with distributed delay and source term without memory term", Boundary Value Problems, 2020(1) (2020), Springer Science and Business Media LLC[DOI]
  3. Abdelbaki Choucha, "Exponential decay of solutions for a viscoelastic coupled Lame system with logarithmic source and distributed delay terms", Mathematical Methods in the Applied Sciences, 44(6), pp.4858~4880 (2021), Wiley[DOI]
  4. Abdelbaki Choucha, "General decay of nonlinear viscoelastic Kirchhoff equation with Balakrishnan‐Taylor damping, logarithmic nonlinearity and distributed delay terms", Mathematical Methods in the Applied Sciences, 44(7), pp.5436~5457 (2021), Wiley[DOI]
  5. Ju. L. Daleckii, "Stability of solutions of differential equations in Banach space" (1974), American Mathematical Society
  6. K.-J. Engel, "One-parameter Semigroups for Linear Evolution Equations" (2000), Springer-Verlag
  7. N. T. Huy, "Exponential dichotomy of evolution equations and admissibility of function spaces on a half-line", J. Funct. Anal, (1), pp.330~354 (2006)[DOI]
  8. J. Kato, "Bounded solutions and periodic solutions to linear differential equations in Banach spaces", Vietnam J. Math, 30(suppl), pp.561~575 (2002)
  9. J. L. Massera, "Linear Eifferential Equations and Function Spaces" (1966), Academic Press
  10. Nguyen Van Minh, "Exponential stability, exponential expansiveness, and exponential dichotomy of evolution equations on the half-line", Integral Equations and Operator Theory, 32(3), pp.332~353 (1998), Springer Science and Business Media LLC[DOI]
  11. R. Nagel, "Evolution equations, semigroups and functional analysis (Milano, 2000)", pp.279~293 (2002), Birkh¨auser
  12. A. Pazy, "Semigroups of Linear Operators and Applications to Partial Differential Equations" (1983), Springer-Verlag

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