Generalized Picone's formula and forced oscillations in quasilinear differential equations of the second order
Archivum mathematicum, Tome 38 (2002) no. 1, pp. 53-59 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

In the paper a comparison theory of Sturm-Picone type is developed for the pair of nonlinear second-order ordinary differential equations first of which is the quasilinear differential equation with an oscillatory forcing term and the second is the so-called half-linear differential equation. Use is made of a new nonlinear version of the Picone’s formula.
In the paper a comparison theory of Sturm-Picone type is developed for the pair of nonlinear second-order ordinary differential equations first of which is the quasilinear differential equation with an oscillatory forcing term and the second is the so-called half-linear differential equation. Use is made of a new nonlinear version of the Picone’s formula.
Classification : 34C10
Keywords: forced quasilinear differential equation of the second order; nonlinear Picone’s identity; Sturmian comparison thorems
@article{ARM_2002_38_1_a5,
     author = {Jaro\v{s}, J. and Kusano, T. and Yoshida, N.},
     title = {Generalized {Picone's} formula and forced oscillations in quasilinear differential equations of the second order},
     journal = {Archivum mathematicum},
     pages = {53--59},
     year = {2002},
     volume = {38},
     number = {1},
     mrnumber = {1899568},
     zbl = {1087.34014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2002_38_1_a5/}
}
TY  - JOUR
AU  - Jaroš, J.
AU  - Kusano, T.
AU  - Yoshida, N.
TI  - Generalized Picone's formula and forced oscillations in quasilinear differential equations of the second order
JO  - Archivum mathematicum
PY  - 2002
SP  - 53
EP  - 59
VL  - 38
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/ARM_2002_38_1_a5/
LA  - en
ID  - ARM_2002_38_1_a5
ER  - 
%0 Journal Article
%A Jaroš, J.
%A Kusano, T.
%A Yoshida, N.
%T Generalized Picone's formula and forced oscillations in quasilinear differential equations of the second order
%J Archivum mathematicum
%D 2002
%P 53-59
%V 38
%N 1
%U http://geodesic.mathdoc.fr/item/ARM_2002_38_1_a5/
%G en
%F ARM_2002_38_1_a5
Jaroš, J.; Kusano, T.; Yoshida, N. Generalized Picone's formula and forced oscillations in quasilinear differential equations of the second order. Archivum mathematicum, Tome 38 (2002) no. 1, pp. 53-59. http://geodesic.mathdoc.fr/item/ARM_2002_38_1_a5/

[1] El-Sayed, M. A.: An oscillation criterion for forced second order linear differential equation. Proc. Amer. Math. Soc. 118 (1993), 813–817. | MR

[2] Graef, J. R., Rankin, S. M., Spikes, P. W.: Oscillation results for nonlinear functional differential equations. Funkcialaj Ekvacioj 27 (1984), 255–260. | MR

[3] Jaroš, J., Kusano, T.: On forced second order half-linear equations. Proceedings of the Symposium on the structure and methods of functional differential equations, RIMS Kokyuroku 984, Kyoto University, 1997, 191–197 (in Japanese).

[4] Jaroš, J., Kusano, T.: A Picone type identity for second order half-linear differential equations. Acta Math. Univ. Comenianae LXVIII (1999), 137–151. | MR

[5] Jaroš, J., Kusano, T.: Forced superlinear oscillations via Picone’s identity. Acta Math. Univ. Comenianae LXIX (2000), 107–113. | MR

[6] Leighton, W.: Comparison theorems for linear differential equations of second order. Proc. Amer. Math. Soc. 13 (1962), 603–610. | MR | Zbl

[7] Nasr, A. H.: Sufficient conditions for the oscillation of forced super-linear second order differential equations with oscillatory potential. Proc. Amer. Math. Soc. 126 (1998), 123–125. | MR | Zbl

[8] Picone, M.: Sui valori eccezionali di un parametro da cui dipende un’equazione differenziale lineare ordinaria del second ordine. Ann. Scuola Nom. Pisa 11 (1910), 1–141.

[9] Rankin, S. M. III: Oscillation theorems for second order nonhomogeneous linear differential equations. J. Math. Anal. Appl. 53 (1976), 550–553. | MR