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<p>A class of dissipative Sturm–Liouville boundary-value problems with eigenparameter-dependent transmission conditions is investigated. By transforming the Sturm–Liouville problem with eigenparameter-dependent transmission conditions to the corresponding linear operator associated with the problem, we prove that this operator is dissipative. Further, certain eigenvalue properties are presented and the theorems on completeness of this operator are established by applying Krein’s theorem.</p>

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On the Dissipative Sturm–Liouville Problem with Transmission Conditions Depending on the Eigenparameter

  • 期刊论文

  • 发表日期：

    2026年5月23日

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  • Fei-fan Li,
  • Ji-jun Ao

摘要

A class of dissipative Sturm–Liouville boundary-value problems with eigenparameter-dependent transmission conditions is investigated. By transforming the Sturm–Liouville problem with eigenparameter-dependent transmission conditions to the corresponding linear operator associated with the problem, we prove that this operator is dissipative. Further, certain eigenvalue properties are presented and the theorems on completeness of this operator are established by applying Krein’s theorem.