Inverse problem of simultaneous determination of the right-hand side and the coefficient in a third-order pseudo-hyperbolic equation with periodic and integral conditions

The inverse boundary value problem with an unknown time-dependent coefficient for a third-order pseudo hyperbolic equation with periodic and integral conditions is studied. When solving the original inverse boundary value problem, the transition from the original inverse problem to some auxiliary inverse problem is carried out. The existence and uniqueness of the solution to an auxiliary problem are proved with the help of contracted mappings. Then the transition to the original inverse problem is made again, as a result, the conclusion is made on the solvability of the original inverse problem.