Application of the ergodic theory to the investigation of a boundaryvalue problem with periodic operator coefficient

  • О. A. Boichuk
  • О. О. Pokutnyi

Abstract

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.
Published
25.03.2013
How to Cite
BoichukО. A., and PokutnyiО. О. “Application of the Ergodic Theory to the Investigation of a Boundaryvalue Problem With Periodic Operator Coefficient”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, no. 3, Mar. 2013, pp. 329-38, http://umj.imath.kiev.ua/index.php/umj/article/view/2422.
Section
Research articles