Linear and nonlinear abstract differential equations of high order

Abstract

The nonlocal boundary value problems for linear and nonlinear degenerate abstract differential equations of arbitrary order are studied. The equations have the variable coefficients and small parameters in principal part. The separability properties for linear problem, sharp coercive estimates for resolvent, discreetness of spectrum and completeness of root elements of the corresponding differential operator are obtained. Moreover, optimal regularity properties for nonlinear problem is established. In application, the separability and spectral properties of nonlocal boundary value problem for the system of degenerate differential equations of infinite order is derived.