二阶非线性时滞方程的振动定理

OSCILLATION THEOREMS FOR SECOND ORDER NONLINEAR DELAY EQUATIONS

本文研究了二阶非线性方程(r(t)x′(t))′+a(t)f(x(τ_1(t))))g(x′(τ_2(t)))=0.的解的振动行为。当a(t)≤0时,我们推广了文献[1]和[2]的结果。当a(b)≥0时。我们得到了一般的结果,文献[3]的结果是我们的特例。

This paper is concerned with the oscillatory behaviour of the solutions of the second order nonlinear delay equation of the form (r(t)x'(t))'+a(t)f(x(τ_1(t)))g(x'(τ_2(t)))=0.In the first part of the Present paper we deal with generalizations of certain results of [1] and [2],where the equation is inostigatcd for a(t)≤ 0;the second part deals with generalizations of certain results of [3].