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# Spectral problem for figure-of-eight graph of Stieltjes strings

### Abstract

We describe the spectrum of the problem generated by the Stieltjes string recurrence relations on a figure-of-eight graph. The continuity and the force balance conditions are imposed at the vertex of the graph. It is shown that the eigenvalues of such (main) problem are interlaced with the elements of the union of sets of eigenvalues of the Dirichlet problems generated by the parts of the string which correspond to the loops of the figure-of-eight graph. Also the eigenvalues of the main problem are interlaced with the elements of the union of sets of eigenvalues of the periodic problems generated by the same parts of the string.

### Article Information

 Title Spectral problem for figure-of-eight graph of Stieltjes strings Source Methods Funct. Anal. Topology, Vol. 16 (2010), no. 4, 349-358 MathSciNet MR2777193 Copyright The Author(s) 2010 (CC BY-SA)

### Authors Information

O. Martinyuk
South-Ukrainian National Pedagogical University, 26 Staroportofrankivs'ka, Odessa, 65023, Ukraine

V. Pivovarchik
South-Ukrainian National Pedagogical University, 26 Staroportofrankivs'ka, Odessa, 65023, Ukraine

### Citation Example

O. Martinyuk and V. Pivovarchik, Spectral problem for figure-of-eight graph of Stieltjes strings, Methods Funct. Anal. Topology 16 (2010), no. 4, 349-358.

### BibTex

@article {MFAT554,
AUTHOR = {Martinyuk, O. and Pivovarchik, V.},
TITLE = {Spectral problem for figure-of-eight graph of Stieltjes strings},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {16},
YEAR = {2010},
NUMBER = {4},
PAGES = {349-358},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=554},
}