We solve a mixed boundary value problem with arbitrary continuous functions, not necessarily satisfying the boundary conditions, in the initial conditions and inhomogeneous terms of the equation We propose a method for finding the Fourier coefficients of auxiliary functions in terms of the Stieltjes integral or the resolvent of a Cauchy operator of the third order.
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A. Yu. Trynin, “Lagrange–Sturm–Liouville processes,” J. Math. Sci. 261, No. 3, 454-486 (2022).
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Translated from Problemy Matematicheskogo Analiza 117, 2022, pp. 111-126.
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Trynin, A.Y. Method for Solving Mixed Boundary Value Problems for Hyperbolic Type Equations by Using Lagrange–Sturm–Liouville Operators. J Math Sci 267, 412–428 (2022). https://doi.org/10.1007/s10958-022-06143-w
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DOI: https://doi.org/10.1007/s10958-022-06143-w