A Problem with Nonlocal Conditions for Partial Differential Equations Unsolved with Respect to the Leading Derivative - Vlasii, O. D.; Ptashnik, B. I. (Ukrains’kyi Matematychnyi Zhurnal, 2003)
In the domain that is the product of a segment and a p-dimensional torus, we investigate the well-posedness of a problem with nonlocal boundary conditions for a partial differential equation unsolved with respect to the leading derivative with respect to a selected variable. We establish conditions for the the classical well-posedness of the problem and prove metric theorems on the lower bounds of small denominators appearing in the course of its solution.