Canonical forms for boundary conditions of self-adjoint odd-order differential operators

Abstract

It is useful to have canonical forms of boundary conditions in the study of the eigenvalues of boundary value problems and associated numerical applications. In [J. Appl. Anal. Comput., 2024, 14(4), {1854--1868}], a canonical form is given for self-adjoint differential operators of even order, with eigenvalue parameter dependent boundary conditions. In this article, we derive canonical forms for the remaining case, namely: for self-adjoint $(2n+1)$-th order differential operators with eigenvalue parameter dependent boundary conditions.

Theorems & Definitions (14)

• Proposition 1
• Theorem 1
• Definition 1
• Remark 1
• Lemma 1
• proof
• Proposition 2
• Theorem 2
• Theorem 3
• proof : Proof of Theorem \ref{['thm:2n+1th-odd']}