On the Coersive Solution of a Defective Boundary Value Problem

ABSTRACT This study addresses boundary value problems for third‐order linear ordinary differential equations with recurring characteristics. By analyzing the principal determinant formed by the boundary conditions, it is shown that the problem is regularly defined with defects within a specific spectral angle; furthermore, the existence of a coercive solution in suitable function spaces for the corresponding non‐homogeneous boundary value problem is proven. The results contribute to the theory of boundary value problems with recurring characteristics and offer methods that can be applied to more general classes of such problems.