Nonlocal problems with an integral boundary condition for the differential equations of odd order

We study the solvability of nonlocal problems for equations
$$u_{ttt} + Au=f(x,t)$$
($0<T<+\infty$, $A$ — elliptic operator) with only two boundary conditions instead of three and with a special integral boundary condition. We prove the existence theorems for regular solutions and indicate a possible generalization of the obtained results.