An inverse spectral problem for second-order functional-differential pencils with two delays
學年 110
學期 1
出版（發表）日期 2021-12-15
作品名稱 An inverse spectral problem for second-order functional-differential pencils with two delays
作品名稱（其他語言）
著者 S.A. Buterin; M.A. Malyugina; C.-T. Shieh
單位
出版者
著錄名稱、卷期、頁數 Applied Mathematics and Computation 411
摘要 Recently, there appeared a considerable interest in inverse Sturm–Liouville-type problems with constant delay. However, necessary and sufficient conditions for solvability of such problems were obtained only in one very particular situation. Here we address this gap by obtaining necessary and sufficient conditions in the case of functional-differential pencils possessing a more general form along with a nonlinear dependence on the spectral parameter. For this purpose, we develop the so-called transformation operator approach, which allows reducing the inverse problem to a nonlinear vectorial integral equation. In Appendix A, we obtain as a corollary the analogous result for Sturm–Liouville operators with delay. Remarkably, the present paper is the first work dealing with an inverse problem for functional-differential pencils in any form. Besides generality of the pencils under consideration, an important advantage of studying the inverse problem for them is the possibility of recovering both delayed terms, which is impossible for the Sturm–Liouville operators with two delays. The latter, in turn, is illustrated even for different values of these two delays by a counterexample in Appendix B. We also provide a brief survey on the contemporary state of the inverse spectral theory for operators with delay observing recently answered long-term open questions.
關鍵字 Functional-differential equation; Pencil; Deviating argument; Constant delay; Inverse spectral problem
語言 en_US
ISSN 1873-5649
期刊性質 國外
收錄於 SCI
產學合作
通訊作者
審稿制度 否
國別 USA
公開徵稿
出版型式 ,電子版,紙本
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機構典藏連結 ( http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/122874 )