Boundary-value problems for linear equations with a generalized invertible operator in a Banach space with basis

Abstract

We consider linear boundary-value problems for operator equations with generalized invertible operators in Banach spaces that have bases. Using the technique of generalized inverse operators applied to generalized invertible operators in Banach spaces, we establish conditions for the solvability of linear boundary-value problems for these operator equations and obtain formulas for the representation of their solutions. We consider special cases of these boundary-value problems, namely, so-called n-and d -normally solvable boundary-value problems as well as normally solvable problems for Noetherian operator equations.