New boundary value problems for fourth-order quasi-hyperbolic equations

In this paper, we study the correctness in the spaces of S.L. Sobolev of new boundary value problems for quasi-hyperbolic differential equations
$$u_{tttt}+Au=f(x,t)$$
($A$ is an elliptic operator acting on spatial variables). For the proposed tasks theorems on the existence and uniqueness of solutions are proved, and examples of non-uniqueness are given.