Electron. J. Differential Equations, Vol. 2017 (2017), No. 287, pp. 1-18.

Direct and inverse Robin-Regge problems

Manfred Moller, Vyacheslav Pivovarchik

The Sturm-Liouville equation is considered on a bounded interval with a Robin boundary condition at the left end and a generalized Regge condition at the right end. Properties of the spectrum of this problem are derived, including the location of the spectrum in the lower half-plane and the asymptotic distribution of the eigenvalues. The inverse problem is solved, given one spectrum or parts of two spectra.

Submitted August 8, 2017. Published November 17, 2017.
Math Subject Classifications: 34B09, 34B07, 34B24, 34L20, 34A55
Key Words: String problem; viscous damping; Robin boundary condition; generalized Regge boundary condition; spectral asymptotics; inverse problems.

Show me the PDF file (310 KB), TEX file for this article.

Manfred Möller
The John Knopfmacher Centre for Applicable Analysis and Number Theory
School of Mathematics
University of the Witwatersrand
Johannesburg, WITS 2050, South Africa
email: manfred.moller@wits.ac.za
Vyacheslav Pivovarchik
Department of Algebra and Geometry
South-Ukrainian National Pedagogocal University
Staroportofrankovskaya str. 26
Odessa, 65020, Ukraine
email: vpivovarchik@gmail.com

Return to the EJDE web page