Correctness of task family with nonclassical boundary conditions

A boundary value problem for partial differential equation with nonlocal boundary relations of special type is resolved by means of a slight modification of the separation of variables method. Ordinal differential operator of the second order subject to boundary conditions of the main problem is not self-adjoint. The system of eigenfunctions generated by the operator has no basis property in $L_2[0,1]$ space. A special system of functions is proposed to expand the solution of the boundary value problem.