The bounded solutions of a second•order difference equation with a jump of the operator coefficient

1Gorodnii, MF, Kravets, VP
1Taras Shevchenko National University of Kyiv
Dopov. Nac. akad. nauk Ukr. 2019, 2:12-16
Section: Mathematics
Language: Ukrainian

We study the problem of existence of the unique bounded solution of a linear secondorder difference equation with a jump of the operator coefficient in a finitedimensional Banach space. For such an equation, the criterion for the existence and uniqueness of a bounded solution is proved for any “input” bounded sequence. The case where the matrix of operator coefficients reduces to a diagonal form is investigated in detail.

Keywords: bounded solution, difference equation, finitedimensional space, linear operator

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