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**Periodic problems of difference equations and ergodic theory.**
*(English)*
Zbl 1222.34074

Summary: Necessary and sufficient conditions for solvability of a family of difference equations with periodic boundary condition were obtained using the notion of relative spectrum of a linear bounded operator in the Banach space and an ergodic theorem. It is shown that when the condition of existence is satisfied, then such periodic solutions are built using the formula for the generalized inverse operator to the linear limited one.

### MSC:

34K10 | Boundary value problems for functional-differential equations |

34K13 | Periodic solutions to functional-differential equations |

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\textit{B. A. Biletskyi} et al., Abstr. Appl. Anal. 2011, Article ID 928587, 12 p. (2011; Zbl 1222.34074)

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### References:

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