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In this article, we consider a nonlocal problem with integral conditions for one-dimensional 4th order partial differential equation. A distinguishing feature of this problem is the presence of integral conditions of the 1st kind. Moreover, the kernels of these conditions depend on both spatial and time variables. We suggest a new approach which enables to overcome the difficulties arising from the form of nonlocal conditions and derive a priori estimates. Obtained estimates play a significant role when we prove the existence and uniqueness of the solution to the problem.
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Л. С. Пулькина (2024) studied this question.
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