Classes of Unique Solvability of Time-Nonlocal Problems for Multidimensional Quasihyperbolic Equations

It is well known that quasihyperbolic equations are associated with the sum of two operators. One of these operators is generated by linear differential expressions depending on time, whereas the other is an elliptic operator with respect to the spatial variables. In this work, the time differential operator is generated by two-point Birkhoff-regular boundary conditions. Meanwhile, the elliptic operator with respect to the spatial variables satisfies the so-called Agmon conditions. For unique solvability, an essential role is played by the mutual location of the spectra of the two operators mentioned above. Moreover, the solvability classes of the problems under consideration depend on the spectrum of the elliptic part of the equation. The work presents classes of unique solvability for a quasihyperbolic equation depending on a particular smoothness in time of its right-hand side.