Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON PERIODICIZING FUNCTIONS

  • Published : 2006.05.01
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Abstract

In this paper we introduce a new concept, a 'periodicizing' function for the linear differential equation with the periodic forcing function. Moreover, we construct this function, which is closely related with the solution of a difference equation and an indefinite sum. Using this function, we can obtain a representation of solutions from which we see immediately the asymptotic behavior of the solutions.

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References

  1. J. Kato, T. Naito, and J. S. Shin, Bounded solutions and periodic solutions to linear differential equations in Banach spaces, Vietnam J. Math.(Proceeding in DEAA) 30 (2002), 561-575
  2. J. Kato, T. Naito, and J. S. Shin, A characterization of solutions in linear differential equations with peri- odic forcing functions, J. Difference Equ. Appl. 11 (2005), no. 1, 1-19 https://doi.org/10.1080/10236190412331317120
  3. K. S. Miller, An Introduction to the Calculus of Finite Differences and Difference Equations, Dover Publications, New York, 1966

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  2. Lyapunov exponents of solutions to linear differential equations with periodic forcing functions vol.342, pp.1, 2008, https://doi.org/10.1016/j.jmaa.2007.09.077
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