Half-linear oscillation criteria: Perturbation in term involving derivative

被引：30

作者：

Dosly, Ondrej ^{[1
]}

Fisnarova, Simona ^{[2
]}

机构：

[1] Masaryk Univ, Dept Math & Stat, CZ-61137 Brno, Czech Republic

[2] Mendel Univ Brno, Dept Math, CZ-61300 Brno, Czech Republic

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2010年 / 73卷 / 12期

关键词：

Half-linear differential equation; Oscillation and nonoscillation criteria; Riccati technique; Perturbation principle; Linearization method; 2ND-ORDER DIFFERENTIAL-EQUATIONS;

D O I：

10.1016/j.na.2010.07.049

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the nonoscillatory half-linear differential equation (r(t)Phi(x'))' + c(t)Phi(x) = 0, Phi(x) := vertical bar x vertical bar(p-2)x, p > 1, and we study oscillatory properties of its perturbation [(r(t) + r(t))Phi(x')]' + (c(t) + c(t))Phi(x) = 0 (*) We use the Riccati technique and relationship between (*) and a certain associated linear equation. The results are applied to the perturbed Euler-type equation. (C) 2010 Elsevier Ltd. All rights reserved.

引用

页码：3756 / 3766

页数：11

共 19 条

[1]

[Anonymous], 2005, N HOLLAND MATH STUDI

[2]

[Anonymous], 2002, Oscillation Theory for Second Order Linear, Half Linear, Superlinear and Sublinear Dynamic Equations

[3]

Diaz J.I., 1985, RES NOTES MATH, V106

[4] Conditionally oscillatory half-linear differential equations [J].

Dosly, O. ;

Uenal, M. .

ACTA MATHEMATICA HUNGARICA, 2008, 120 (1-2) :147-163

[5] Integral characterization of the principal solution of half-linear second order differential equations [J].

Dosly, O ;

Elbert, A .

STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA, 2000, 36 (3-4) :455-469

[6]

DOSLY O, 2006, HIROSHIMA MATH J, V36, P203

[7]

DOSLY O, VARIATIONAL TE UNPUB

[8]

Dosly O., 2003, ARCH MATH BRNO, V39, P233

[9] Perturbations of the half-linear Euler-Weber type differential equation [J].

Dosly, Ondrej .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 323 (01) :426-440

[10] A linearization method in oscillation theory of half-linear second-order differential equations [J].

Dosly, Ondrej ;

Pena, Simon .

JOURNAL OF INEQUALITIES AND APPLICATIONS, 2005, 2005 (05) :535-545

← 1 2 →