Geodesic
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

DOI

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/}
}
TY  - JOUR
AU  - Beesack, Paul R.
TI  - On Sturm's Separation Theorem
JO  - Canadian mathematical bulletin
PY  - 1972
SP  - 481
EP  - 487
VL  - 15
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1972-086-7/
DO  - 10.4153/CMB-1972-086-7
ID  - 10_4153_CMB_1972_086_7
ER  - 
%0 Journal Article
%A Beesack, Paul R.
%T On Sturm's Separation Theorem
%J Canadian mathematical bulletin
%D 1972
%P 481-487
%V 15
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1972-086-7/
%R 10.4153/CMB-1972-086-7
%F 10_4153_CMB_1972_086_7

Cité par Sources :