Boundary-Value Problems for Some Higher-Order Nonclassical Differential Equations

The paper consists of two parts. The first part deals with the solvability of new boundary-value problems for the model quasihyperbolic equations
\begin{equation*} (-1)^pD^{2p}_tu=Au+f(x,t), \end{equation*}
where $p>1$, for a self-adjoint second-order elliptic operator $A$. For the problems under study, the existence and uniqueness theorems are proved for regular solutions. In the second part, the results obtained in the first part are somewhat sharpened and generalized.