Boundary value problems of quaternion-valued differential equations: solvability and Green’s function

Abstract

Abstract This paper is associated with Sturm–Liouville type boundary value problems and periodic boundary value problems for quaternion-valued differential equations (QDEs). Employing the theory of quaternionic matrices, we prove the conditions for the solvability of the linear boundary valued problem and find Green’s function.

Keywords

• Sturm–Liouville boundary value problem
• Periodic boundary value problem
• Green’s function
• Quaternion-valued differential equation