Uniform separable differential operators with parameters

In this paper we study boundary value problems for anisotropic partial differential-operator equations with parameters. The principal part of the appropriate differential operators are not self-adjoint. Several conditions for the uniform separability in weighted Banach-valued L p -spaces are given. Sharp estimates for the resolvent of the corresponding differential operator are obtained. In particular the positivity and R-positivity of these operators are established. As an application we study the separability of degenerate DOEs, maximal regularity for degenerate abstract parabolic problem with parameters, the uniform separability of finite and infinite systems for degenerate anisotropic partial differential equations with parameters.