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    jsp.display-item.identifier=請使用永久網址來引用或連結此文件: https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/122642

    题名: An inverse spectral problem for second-order functional-differential pencils with two delays
    作者: Buterin, S.A.;Malyugina, M.A.;Shieh, C.-T.
    关键词: Functional-differential equation;Pencil;Deviating argument;Constant delay;Inverse spectral problem
    日期: 2021-12-15
    上传时间: 2022-04-13 12:11:14 (UTC+8)
    出版者: Elsevier
    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.
    關聯: Applied Mathematics and Computation 411, 126475
    DOI: 10.1016/j.amc.2021.126475
    显示于类别:[數學學系暨研究所] 期刊論文


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