Trace Formulae for Second-Order Differential Pencils with a Frozen Argument

Yi-Teng Hu () and Murat Şat
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Yi-Teng Hu: School of Mathematics and Statistics, Xidian University, Xi’an 710126, China
Murat Şat: Department of Mathematics, Faculty of Science and Art, Erzincan Binali Yildirim University, Erzincan 24100, Turkey

Mathematics, 2023, vol. 11, issue 18, 1-7

Abstract: This paper deals with second-order differential pencils with a fixed frozen argument on a finite interval. We obtain the trace formulae under four boundary conditions: Dirichlet–Dirichlet, Neumann–Neumann, Dirichlet–Neumann, Neumann–Dirichlet. Although the boundary conditions and the corresponding asymptotic behaviour of the eigenvalues are different, the trace formulae have the same form which reveals the impact of the frozen argument.

Keywords: differential pencils; regularized trace formulae; frozen argument (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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