Об однозначной разрешимости регулярного решения уравнения смешанного типа второго рода четвертого порядка с нелокальными краевыми условиями периодического типа

This paper investigates the unique solvability of a regular generalized solution to a periodic-type
nonlocal boundary value problem for a fourth order mixed-type equations of the second kind in a
Sobolev space. Using the modified Galerkin method, a priori estimates, and the "ε-regularization"
method, the existence and uniqueness of the solution are proven. An auxiliary fifth-order equation
with a small parameter is considered, for which a priori estimates are also established.
The results are based on the application of the energy integral method and the concept of
weak compactness, which provides justification for the convergence of solutions under the limiting
transition. The study is grounded in the works of V.N. Vragov, I.E. Egorov, S.Z. Dzhamalov, and
other researchers devoted to mixed-type equations and nonlocal boundary problems.