B-Separable boundary value problems in Banach-valued function spaces

In this paper, the nonlocal boundary value problems for anisotropic partial differential-operator equations with dependent coefficients in Banach-valued Besov (B) spaces are studied. The principal parts of the appropriate differential operators are non-self-adjoint. Several conditions for separability and Fredholmness are given. These results permit us to establish that the inverse of the corresponding differential operators belong to the Schatten q-class. The spectral properties of the appropriate differential operators are also investigated. In addition we study the maximal regularity of nonlocal initial boundary value problems for abstract parabolic equations, finite or infinite systems of parabolic equations and the separability of nonlocal boundary value problems for finite or infinite systems of quasi-elliptic equations in B spaces.