Linear boundary value problems for normally solvable operator equations in a Banach space
А. М. Самойленко, А. А. Бойчук, В. Ф. Журавлев · Differential Equations · 2014
We consider linear boundary value problems for operator equations with generalized-invertible operator in a Banach or Hilbert space. We obtain solvability conditions for such problems and indicate the structure of their solutions. We construct a generalized Green operator and analyze its properties and the relationship with a generalized inverse operator of the linear boundary value problem. The suggested approach is illustrated in detail by an example.