The precise mathematical investigation of various natural phenomena is an old and difficult problem. This book is the first to deal systematically with the general non-selfadjoint problems in mechanics and physics. It deals mainly with bounded domains with smooth boundaries, but also considers elliptic boundary value problems in tube domains, i.e. in non-smooth domains. This volume will be of particular value to those working in differential equations, functional analysis, and equations of mathematical physics.
Table of Contents
Part 1 Auxiliary results: general notions from functional analysis; interpolation of spaces and operators. Part 2 Unbounded polynomial operator pencils: completeness of root vectors of an operator from the class rhop(H); completeness of root vectors of an unbounded operator; n-fold completeness of root vectors of an unbounded polynomial operator pencil; n-fold completeness of root vectors of a system of unbounded polynomial operator pencils; the completeness of root vectors of the system of unbounded linear operator pencils. Part 3 In principal the multipoint problem for ordinary differential equation with polynomial parameter: p-regular functional conditions; coerciveness of principally of multipoint problems for ordinary differential equations with a polynomial parameter; fold completeness of root functions for in principally multipoint problems for ordinary differential equations with a polynomial parameter; completeness of root functions for in principally multipoint problems for ordinary differential equations with a linear parameter. Part 4 Principally elliptic boundary-value problem with a polynomial parameter: principally regular elliptic boundary-value problems with a polynomial parameter; irregular elliptic boundary-value problems for the Laplace equations. Part 5 Differential-operator equations: differential-operator equations on the whole axis; Cauchy problem for parabolic differential-operator equations; boundary-value problems for elliptic differential - operator equations; completeness of elementary solutions of differential-operator equations. Part 6 Partial differential equations: principally initial-boundary value problems for parabolic equations; boundary-value problems for elliptic equations of the 4-th order.