TY - JOUR
AU - О. A. Boichuk
AU - О. О. Pokutnyi
PY - 2013/03/25
Y2 - 2023/03/27
TI - Application of the ergodic theory to the investigation of a boundaryvalue problem with periodic operator coefficient
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 65
IS - 3
SE - Research articles
DO -
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/2422
AB - We establish necessary and sufficient conditions for the solvability of a family of differential equations with periodic operator coefficient and periodic boundary condition by using the notion of the relative spectrum of a linear bounded operator in a Banach space and the ergodic theorem. We show that if the existence condition is satisfied, then these periodic solutions can be constructed by using the formula for the generalized inverse of a linear bounded operator obtained in the present paper.
ER -