On a Nonlocal Boundary Value Problem for Linear Differential Equations of Changing Type. Hyperbolic-Parabolic Equations, Antiperiodic Solutions

摘要

A nonlocal boundary value problem for a class of linear partial differential equations of second order in a bounded domain {(x′ ,x_m) ∈ R~m : x′= (x_1,...,x_(m-1)) ∈ D, 0 < x_m < h} is investigated. Uniqueness of a weak solution is proved. Examples for non-uniqueness of the solutions of the wave equation in the case of nonlocal conditions u(x′ , h) = —u(x′ , 0), u_x_m (x′ , h) = -u_x_m (x′ , 0) in D is given. The case of antiperiodic solutions is also considered.