caa a22 4500 388109106 CHVBK 20180307125348.0 cr unu---uuuuu 161130s1999 xx s 000 0 eng 10.1017/S0308210500013093 doi S0308210500013093 pii (NATIONALLICENCE)cambridge-10.1017/S0308210500013093 Sturm—Liouville problems and discontinuous eigenvalues [Elektronische Daten] If a Sturm—Liouville problem is given in an open interval of the real line, then regular boundary value problems can be considered on compact sub-intervals. For these regular problems, all with necessarily discrete spectra, the eigenvalues depend on both the end-points of the compact intervals, and upon the choice of the real separated boundary conditions at these end-points. These eigenvalues are not, in general, continuous functionsof the end-points and boundary conditions. The paper shows the surprising form of these discontinuities. The results have applications to the approximations of singular Sturm—Liouville problems by regular problems, and to the theoretical aspects of the Sleign2 Computer program. Copyright © Royal Society of Edinburgh 1999 Everitt W. N. School of Mathematics and Statistics, University of Birmingham, Egdbaston, Birmingham B15 2TT, UK (w.n.everitt@bham.ac.uk) Möller M. Department of Mathematics, University of the Witwatersrand, Wits 2050, Republic of South Africa (036man@cosmos.wits.ac.za) Zettl A. Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115-2888, USA (zettl@math.niu.edu) Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/4(1999), 707-716 0308-2105 129:4<707 1999 129 PRM https://doi.org/10.1017/S0308210500013093 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0308210500013093 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Everitt W. N. School of Mathematics and Statistics, University of Birmingham, Egdbaston, Birmingham B15 2TT, UK (w.n.everitt@bham.ac.uk) NATIONALLICENCE 700 1- Möller M. Department of Mathematics, University of the Witwatersrand, Wits 2050, Republic of South Africa (036man@cosmos.wits.ac.za) NATIONALLICENCE 700 1- Zettl A. Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115-2888, USA (zettl@math.niu.edu) NATIONALLICENCE 773 0- Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/4(1999), 707-716 0308-2105 129:4<707 1999 129 PRM CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge