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Abstract
This article investigates the conditional correctness of a boundary value problem for a third-order differential equation of structured type. Boundary and Cauchy-type problems associated with higher-order differential equations are often not well-posed in the sense of Hadamard, meaning that even when existence and uniqueness of a solution are guaranteed, the stability condition may fail. The paper analyzes the causes of such ill-posedness, introduces the concept of conditional correctness, and examines the application of a priori estimates, the method of fundamental solutions, Green function, and regularization techniques to ensure stability. The obtained results are essential for the analysis and determination of stable solutions of higher-order differential equations.
References
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