On the issue of solubility of one boundary-value problem for a pseudohyperbolic quartic with an additional integral condition

The article investigates an inverse problem for a pseudohyperbolic quartic with periodical boundary conditions. At first the initial problem is reduced to an equivalent problem, for which the author proves the theorem of existence and uniqueness. Then on the basis of these facts the researcher proves the existence and uniqueness of the classical solution of the initial problem.