A nonlocal boundary-value problem for a fourth-order mixed-type equation
Kudratillo FayazovTurin Polytechnic University in Tashkent, Tashkent, UzbekistanK. O.National University of Uzbekistan, Tashkent, Uzbekistan Turin Polytechnic University in Tashkent, Tashkent, Uzbekistan
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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 L_2, 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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