Nonlinear Inverse Problem for a Sixth Order Differential Equation with Two Redefinition Functions
T. K. YuldashevNational University of Uzbekistan, Uzbek-Israel Joint Faculty of High Technology and Engineering Mathematics, 100174, Tashkent, UzbekistanO. Sh. KilichevV.I. Romanovskii Institute Mathematics, Academy of Sciences of Uzbekistan, 100174, Tashkent, Uzbekistan
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Аннотация
In this paper, we consider an inhomogeneous sixth-order partial differential equation with two redefinition functions at the end point of the given segment. These redefinition functions enter nonlinearly into partial differential equation. The Fourier method of separation of variables is applied. Absolutely and uniformly convergence of Fourier series are proved. The Cauchy–Schwartz inequalities and the Bessel inequality are used. Theorems on the unique solvability of inverse problems are proved. The method of successive approximations is used in combination with the method of contraction mappings.
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