Inverse problem for differential systems having a singularity and turning point of even or odd order

Year 2023, Volume: 52 Issue: 5, 1239 - 1253, 31.10.2023

Seyfollah Mosazadeh

https://doi.org/10.15672/hujms.1050832

Abstract

In this paper, the canonical property of the solutions and the inverse problem for a system of differential equations having a singularity and turning point of even or odd order are investigated. First, we study the infinite product representation of the solutions of the system in turning case, and derive the corresponding dual equations. Then, by a replacement, we transform the system of differential equations to a second-order differential equation with a singularity and find the canonical product representation of its solution, and provide a procedure for constructing the solution of the inverse problem. We present a new approach to solve the inverse problems having a singularity inside the interval.

Keywords

Maxwell’s equations, singularity, turning point, dual equations, factorization theorem

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