A characteristic feature of realizability of nonstationary differential systems in Banach spaces

摘要

M-operators, a characteristic feature of quasilinear nonstationary differential equations of state in Banach space, are discussed. A Banach coset space of μ-equivalence classes of all Bochner integrable mappings is considered. The problem of quasilinear realization is solvable if and only if the operator is extendable. The operator is extendable if and only if the class contains a function such that the fulfillment of μ-relation can be ensured. A set Q in a vector space L is said to be absorbing if, for any vector, there exists a real number. Extendability of the operator is found to be equivalent to the simultaneous fulfillment of some necessary conditions.