| Title:
|
Generalized Picone's formula and forced oscillations in quasilinear differential equations of the second order (English) |
| Author:
|
Jaroš, J. |
| Author:
|
Kusano, T. |
| Author:
|
Yoshida, N. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
38 |
| Issue:
|
1 |
| Year:
|
2002 |
| Pages:
|
53-59 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
forced quasilinear differential equation of the second order |
| Keyword:
|
nonlinear Picone’s identity |
| Keyword:
|
Sturmian comparison thorems |
| MSC:
|
34C10 |
| idZBL:
|
Zbl 1087.34014 |
| idMR:
|
MR1899568 |
| . |
| Date available:
|
2008-06-06T22:29:50Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107819 |
| . |
| Reference:
|
[1] El-Sayed, M. A.: An oscillation criterion for forced second order linear differential equation.Proc. Amer. Math. Soc. 118 (1993), 813–817. MR 1154243 |
| Reference:
|
[2] Graef, J. R., Rankin, S. M., Spikes, P. W.: Oscillation results for nonlinear functional differential equations.Funkcialaj Ekvacioj 27 (1984), 255–260. MR 0775209 |
| Reference:
|
[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). |
| Reference:
|
[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 1711081 |
| Reference:
|
[5] Jaroš, J., Kusano, T.: Forced superlinear oscillations via Picone’s identity.Acta Math. Univ. Comenianae LXIX (2000), 107–113. MR 1796791 |
| Reference:
|
[6] Leighton, W.: Comparison theorems for linear differential equations of second order.Proc. Amer. Math. Soc. 13 (1962), 603–610. Zbl 0118.08202, MR 0140759 |
| Reference:
|
[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. Zbl 0891.34038, MR 1451823 |
| Reference:
|
[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. |
| Reference:
|
[9] Rankin, S. M. III: Oscillation theorems for second order nonhomogeneous linear differential equations.J. Math. Anal. Appl. 53 (1976), 550–553. MR 0402186 |
| . |
