Nonlocal problem with integral condition for a fourth order equation

In this paper, we consider a nonlocal problem with integral condition with respect to spacial variable for a forth order partial differential equation. The conditions on the data for unique solvability of the problem in Sobolev space are determined. Proving of uniqueness of generalized solution is based on acquired apriori estimates. To prove the solvability we use a following scheme: sequence of approximate solutions using Galerkin procedure is built, apriory estimates that allow to extract from it a convergent subsequence are received, on the final stage it is shown that the limit of subsequence is the required generalized solution.