Ilkiv V. Nonlocal boundary-value problems for partial differential equations and differential-operator equations

Dissertation deals with the study of nonlocal two-point and multipoint problems for the typeless linear differential equations and systems with constant, variable and pseudodifferential coefficients, of an arbitrary (also infinite) order, in the domain which is a Cartesian product of a segment and a multidimensional torus. The solution of such problems is generally non-unique, and even if unique, it does not exist in a scale of Sobolev spaces (periodical functions) or other spaces. The ill-posedness in a sense of Hadamard of the problems considered is caused by the problem of small denominators which appear in the Fourier series representing formal solutions of the nonlocal problems.