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SOME OSCILLATION CRITERIA FOR SECOND ORDER NONLINEAR FUNCTIONAL ORDINARY DIFFERENTIAL EQUATIONS

E.M.E. Zayed; M.A. El-Moneam   

  1. Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt
  • 收稿日期:2004-11-02 修回日期:2005-08-29 出版日期:2007-07-20 发布日期:2007-07-20
  • 通讯作者: E.M.E. Zayed

SOME OSCILLATION CRITERIA FOR SECOND ORDER NONLINEAR FUNCTIONAL ORDINARY DIFFERENTIAL EQUATIONS

E.M.E. Zayed; M.A. El-Moneam   

  1. Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt
  • Received:2004-11-02 Revised:2005-08-29 Online:2007-07-20 Published:2007-07-20
  • Contact: E.M.E. Zayed

摘要:

The main objective of this article is to study the oscillatory behavior of the
solutions of the following nonlinear functional differential equations
(a(t)x'(t))'+δ1p(t)x'(t)+δ2q(t)f(x(g(t)))=0,
for 0≤ t0 ≤t, where δ1=± 1 and δ2=± 1. The functions p,q,g:[t0,∞ )→R, f:R→R are continuous, a(t)>0, p(t)≥0,q(t)≥0 for t≥t0,limt→∞g(t)=∞, and q is not identically zero on any subinterval of [t0,∞). Moreover, the functions
q(t),g(t), and a(t) are continuously differentiable.

关键词: Oscillatory and nonoscillatory solutions, nonlinear functional differential equations

Abstract:

The main objective of this article is to study the oscillatory behavior of the
solutions of the following nonlinear functional differential equations
(a(t)x'(t))'+δ1p(t)x'(t)+δ2q(t)f(x(g(t)))=0,
for 0≤ t0 ≤t, where δ1=± 1 and δ2=± 1. The functions p,q,g:[t0,∞ )→R, f:R→R are continuous, a(t)>0, p(t)≥0,q(t)≥0 for t≥t0,limt→∞g(t)=∞, and q is not identically zero on any subinterval of [t0,∞). Moreover, the functions
q(t),g(t), and a(t) are continuously differentiable.

Key words: Oscillatory and nonoscillatory solutions, nonlinear functional differential equations

中图分类号: 

  • 34K10