Hiroshima Mathematical Journal

Oscillation and nonoscillation of certain second order quasilinear dynamic equations

Zhiting Xu and Yuanfeng Wang

Full-text: Open access

Abstract

We establish new oscillation and nonoscillation theorems for the second order quasilinear dynamic equation

(r(t)|y^{\Delta}(t)|^{\alpha-1}y^{\Delta}(t))^{\Delta}+f(t,y^{\sigma}(t))=0

on a time scale $\T$. Our results not only extend the results given in J. Wang, "On second order quasilinear oscillations," Funkcialaj Ekvacioj, 41 (1998), 25-54, but also unify the oscillation and nonoscillation criteria for second order quasilinear differential equations and difference equations.

Article information

Source
Hiroshima Math. J., Volume 42, Number 3 (2012), 385-409.

Dates
First available in Project Euclid: 11 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1355238374

Digital Object Identifier
doi:10.32917/hmj/1355238374

Mathematical Reviews number (MathSciNet)
MR3050127

Zentralblatt MATH identifier
1266.34145

Subjects
Primary: 34K11: Oscillation theory 39A10: Difference equations, additive
Secondary: 39A99: None of the above, but in this section 34N05: Dynamic equations on time scales or measure chains {For real analysis on time scales or measure chains, see 26E70}

Keywords
Oscillation nonoscillation quasilinear dynamic equations time scale second order

Citation

Xu, Zhiting; Wang, Yuanfeng. Oscillation and nonoscillation of certain second order quasilinear dynamic equations. Hiroshima Math. J. 42 (2012), no. 3, 385--409. doi:10.32917/hmj/1355238374. https://projecteuclid.org/euclid.hmj/1355238374


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