The theory of differential-operator equations is one of two modern theories for the study of both ordinary and partial differential equations, with numerous applications in mechanics and theoretical physics. Although a number of published works address differential-operator equations of the first and second orders, to date none offer a treatment of the higher orders.
In Differential-Operator Equations, the authors present a systematic treatment of the theory of differential-operator equations of higher order, with applications to partial differential equations. They construct a theory that allows application to both regular and irregular differential problems. In particular, they study problems that cannot be solved by various known methods and irregular problems not addressed in existing monographs. These include Birkhoff-irregularity, non-local boundary value conditions, and non-smoothness of the boundary of the domains.
Among this volume's other points of interest are:
Completeness and the Abel Basis Property of a System of Root Vectors
Principally Boundary Value Problems for Ordinary Differential Equations with a Polynomial Parameter
Principally Regular Elliptic Boundary Value Problems with a Polynomial Parameter
Elliptic Differential-Operator Equations
Hyperbolic Differential-Operator Equations
Parabolic Differential-Operator Equations
Well-Posed Problems for Partial Differential Equations
List of Notations