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Abstract
This thesis studies the conditional correctness of a boundary value problem posed for a third-order structured-type differential equation. Boundary and Cauchy-type problems associated with higher-order differential equations are often not well-posed in the sense of Hadamard that is, even when the existence and uniqueness of a solution are guaranteed, the stability condition may fail. The thesis analyzes the causes of such ill-posedness, substantiates the concept of conditional correctness, and examines the application of a priori estimates, the method of fundamental solutions, the Green's function, and regularization techniques to ensure stability. The obtained results are of significant importance for analyzing and determining stable solutions of higher-order differential equations.
References
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