On Sturm's Separation Theorem
Canadian mathematical bulletin, Tome 15 (1972) no. 4, pp. 481-487
Voir la notice de l'article provenant de la source Cambridge University Press
The purpose of this note is to obtain an extension of the classical Sturm separation theorem for the second order, linear selfadjoint differential equation 1 to the case of a noncompact interval. The classical theorem (cf. [3, p. 209], [4, p. 224]) assumes that r and s are continuous with r positive on a compact interval I, and concludes that between each pair of zeros (on I) of one (nontrivial) solution of (1) there lies precisely one zero of any other linearly independent solution of (1). If I is not compact, a function y which is a solution of (1) on /may often be extended (continuously) to an endpoint, say a, of I.
Beesack, Paul R. On Sturm's Separation Theorem. Canadian mathematical bulletin, Tome 15 (1972) no. 4, pp. 481-487. doi: 10.4153/CMB-1972-086-7
@article{10_4153_CMB_1972_086_7,
author = {Beesack, Paul R.},
title = {On {Sturm's} {Separation} {Theorem}},
journal = {Canadian mathematical bulletin},
pages = {481--487},
year = {1972},
volume = {15},
number = {4},
doi = {10.4153/CMB-1972-086-7},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1972-086-7/}
}
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