This paper is devoted to studying the unique solvability of the inverse boundary-value problem of finding the coefficients in a fourth order pseudo-hyperbolic equation with nonlocal boundary and nonlocal integral conditions. First, the original problem reduces to the corresponding equivalent problem. Further, using the Fourier method, the equivalent problem is reduced to the system of integral equations. Our proof of existence and uniqueness to the solution of the system of integral equations relies on the contraction mapping principle. On the basis of the equivalence of these problems, the theorem of the existence and uniqueness of the classical solution is proved.

nonlocal inverse problem, pseudo-hyperbolic equation, Fourier method, integral condition, classic solution.

Received: October 21, 2020; Revised: November 3, 2020; Accepted: November 30, 2020; Published: February 15, 2021

How to cite this article: Elvin I. Azizbayov, The unique solvability of a nonlocal inverse boundary-value problem for the pseudo-hyperbolic equation of fourth order, Advances in Differential Equations and Control Processes 24(1) (2021), 79-100. DOI: 10.17654/DE024010079

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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