A comparison theorem and oscillation criteria for second-order nonlinear differential equations

被引：7

作者：

Yamaoka, Naoto ^{[1
]}

机构：

[1] Osaka Prefecture Univ, Dept Math Sci, Sakai, Osaka 5998531, Japan

来源：

APPLIED MATHEMATICS LETTERS | 2010年 / 23卷 / 08期

关键词：

Oscillation; Nonlinear differential equations; Comparison theorem; Phase plane analysis; P-LAPLACIAN;

D O I：

10.1016/j.aml.2010.04.007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper presents a new comparison theorem for the oscillation of solutions of second-order nonlinear differential equations of the form (phi(p)(x'))' + 1/t(p) f(x) = 0, where p > 1 and phi(p)(x) = vertical bar x vertical bar(p-2)x and f (x) satisfies the signum condition xf (x) > 0 if x not equal 0, but is not assumed to be monotone. Combining the comparison theorem and known oscillation criteria, we can also derive new oscillation criteria for the equations. Proof is established by means of phase plane analysis of systems. (c) 2010 Elsevier Ltd. All rights reserved.

引用

页码：902 / 906

页数：5

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