Abstract
The criterion of uniqueness of a solution of the problem with periodicity and nonlocal and boundary conditions is established by the spectral analysis for a fourth-order mixed-type equation in a rectangular region. When constructing a solution in the form of the sum of a series, we use the completeness in the space L2; the system of eigenfunctions of the corresponding problem orthogonally conjugate. When proving the convergence of a series, the problem of small denominators arises. Under some conditions imposed on the parameters of the data of the problem and given functions, the stability of the solution is proved.
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Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 17, No. 1, pp. 30–41 January–March, 2020.
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Fayazov, K.S., Khajiev, I.O. A nonlocal boundary-value problem for a fourth-order mixed-type equation. J Math Sci 248, 166–174 (2020). https://doi.org/10.1007/s10958-020-04866-2
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DOI: https://doi.org/10.1007/s10958-020-04866-2