Oscillation constants for second-order nonlinear dynamic equations of Euler type on time scales

被引：17

作者：

Rehak, Pavel ^{[1
]}

Yamaoka, Naoto ^{[2
]}

机构：

[1] Brno Univ Technol, Inst Math, Fac Mech Engn, Brno, Czech Republic

[2] Osaka Prefecture Univ, Dept Math Sci, Sakai, Osaka, Japan

来源：

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS | 2017年 / 23卷 / 11期

关键词：

Oscillation constant; dynamic equations on time scales; Euler-Cauchy equation; Riccati technique; phase plane analysis; Schauder fixed point theorem; Primary: 34N05; Secondary: 34C10; DIFFERENTIAL-EQUATIONS;

D O I：

10.1080/10236198.2017.1371146

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We are concerned with the oscillation problem for second-order nonlinear dynamic equations on time scales of the form, where f(x) satisfies if . By means of Riccati technique and phase plane analysis of a system, (non)oscillation criteria are established. A necessary and sufficient condition for all nontrivial solutions of the Euler-Cauchy dynamic equation +./( ts( t)) y = 0 to be oscillatory plays a crucial role in proving our results.

引用

页码：1884 / 1900

页数：17

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