On the dissipative Sturm–Liouville problem with transmission conditions depending on the eigenparameter

Authors

  • Fei-fan Li College of Sciences, Inner Mongolia University of Technology, Hohhot, China
  • Ji-jun Ao College of Sciences, Inner Mongolia University of Technology, Hohhot, China

DOI:

https://doi.org/10.3842/umzh.v78i3-4.9398

Keywords:

Sturm-Liouville problem, dissipative differential operator, eigenparameter-dependent transmission conditions, completeness theorems

Abstract

UDC 517.927, 517.98

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.

References

The full version of this paper will be published in Ukrainian Mathematical Journal, Vol. 78, No. 3-4, 2026.

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Published

28.03.2026

Issue

Vol. 78 No. 3-4 (2026)

Section

Research articles