Problems with one quarter
Czechoslovak Mathematical Journal, Tome 55 (2005) no. 2, pp. 349-363
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

In this paper two sequences of oscillation criteria for the self-adjoint second order differential equation $(r(t)u^{\prime }(t))^{\prime }+p(t)u(t)=0$ are derived. One of them deals with the case $\int ^{\infty }\frac{{\mathrm d}t}{r(t)}=\infty $, and the other with the case $\int ^{\infty }\frac{{\mathrm d}t}{r(t)}\infty $.
In this paper two sequences of oscillation criteria for the self-adjoint second order differential equation $(r(t)u^{\prime }(t))^{\prime }+p(t)u(t)=0$ are derived. One of them deals with the case $\int ^{\infty }\frac{{\mathrm d}t}{r(t)}=\infty $, and the other with the case $\int ^{\infty }\frac{{\mathrm d}t}{r(t)}\infty $.
Classification : 34C10
Keywords: oscillation theory
@article{CMJ_2005_55_2_a5,
     author = {Ohriska, J\'an},
     title = {Problems with one quarter},
     journal = {Czechoslovak Mathematical Journal},
     pages = {349--363},
     year = {2005},
     volume = {55},
     number = {2},
     mrnumber = {2137142},
     zbl = {1081.34033},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2005_55_2_a5/}
}
TY  - JOUR
AU  - Ohriska, Ján
TI  - Problems with one quarter
JO  - Czechoslovak Mathematical Journal
PY  - 2005
SP  - 349
EP  - 363
VL  - 55
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/CMJ_2005_55_2_a5/
LA  - en
ID  - CMJ_2005_55_2_a5
ER  - 
%0 Journal Article
%A Ohriska, Ján
%T Problems with one quarter
%J Czechoslovak Mathematical Journal
%D 2005
%P 349-363
%V 55
%N 2
%U http://geodesic.mathdoc.fr/item/CMJ_2005_55_2_a5/
%G en
%F CMJ_2005_55_2_a5
Ohriska, Ján. Problems with one quarter. Czechoslovak Mathematical Journal, Tome 55 (2005) no. 2, pp. 349-363. http://geodesic.mathdoc.fr/item/CMJ_2005_55_2_a5/

[1] J. H. Barrett: Oscillation theory of ordinary linear differential equations. Adv. Math. 3 (1969), 415–509. | DOI | MR | Zbl

[2] M. Cecchi, M. Marini and G. Villari: Integral criteria for a classification of solutions of linear differential equations. J.  Differential Equations 99 (1992), 381–397. | DOI | MR

[3] J. Dzurina: Property  (A) of advanced functional differential equations. Math. Slovaca 45 (1995), 129–137. | MR | Zbl

[4] P. Hartman: Ordinary Differential Equations. Wiley, New York, 1964. | MR | Zbl

[5] J. Ohriska: Oscillation of differential equations and $v$-derivatives. Czechoslovak Math.  J. 39(114) (1989), 24–44. | MR | Zbl

[6] J. Ohriska: On the oscillation of a linear differential equation of second order. Czechoslovak Math. J. 39(114) (1989), 16–23. | MR | Zbl

[7] W. T. Reid: Sturmian Theory for Ordinary Differential Equations. Springer-Verlag, New York, 1980. | MR | Zbl

[8] D. Willett: Classification of second order linear differential equations with respect to oscillation. Adv. Math. 3 (1969), 594–623. | DOI | MR | Zbl