Generalized Picone's formula and forced oscillations in quasilinear differential equations of the second order

Jaroslav Jaroš; Takaŝi Kusano; N. Yoshida

Archivum Mathematicum (2002)

  • Volume: 038, Issue: 1, page 53-59
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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Jaroš, Jaroslav, Kusano, Takaŝi, and Yoshida, N.. "Generalized Picone's formula and forced oscillations in quasilinear differential equations of the second order." Archivum Mathematicum 038.1 (2002): 53-59. <http://eudml.org/doc/248924>.

@article{Jaroš2002,
abstract = {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.},
author = {Jaroš, Jaroslav, Kusano, Takaŝi, Yoshida, N.},
journal = {Archivum Mathematicum},
keywords = {forced quasilinear differential equation of the second order; nonlinear Picone’s identity; Sturmian comparison thorems; forced quasilinear differential equation of the second order; nonlinear Picone's identity; Sturmian comparison thorems},
language = {eng},
number = {1},
pages = {53-59},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Generalized Picone's formula and forced oscillations in quasilinear differential equations of the second order},
url = {http://eudml.org/doc/248924},
volume = {038},
year = {2002},
}

TY - JOUR
AU - Jaroš, Jaroslav
AU - Kusano, Takaŝi
AU - Yoshida, N.
TI - Generalized Picone's formula and forced oscillations in quasilinear differential equations of the second order
JO - Archivum Mathematicum
PY - 2002
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 038
IS - 1
SP - 53
EP - 59
AB - 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.
LA - eng
KW - forced quasilinear differential equation of the second order; nonlinear Picone’s identity; Sturmian comparison thorems; forced quasilinear differential equation of the second order; nonlinear Picone's identity; Sturmian comparison thorems
UR - http://eudml.org/doc/248924
ER -

References

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  1. An oscillation criterion for forced second order linear differential equation, Proc. Amer. Math. Soc. 118 (1993), 813–817. MR1154243
  2. Oscillation results for nonlinear functional differential equations, Funkcialaj Ekvacioj 27 (1984), 255–260. MR0775209
  3. 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. A Picone type identity for second order half-linear differential equations, Acta Math. Univ. Comenianae LXVIII (1999), 137–151. MR1711081
  5. Forced superlinear oscillations via Picone’s identity, Acta Math. Univ. Comenianae LXIX (2000), 107–113. MR1796791
  6. Comparison theorems for linear differential equations of second order, Proc. Amer. Math. Soc. 13 (1962), 603–610. Zbl0118.08202MR0140759
  7. Sufficient conditions for the oscillation of forced super-linear second order differential equations with oscillatory potential, Proc. Amer. Math. Soc. 126 (1998), 123–125. Zbl0891.34038MR1451823
  8. 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. Oscillation theorems for second order nonhomogeneous linear differential equations, J. Math. Anal. Appl. 53 (1976), 550–553. MR0402186

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