偶数阶非线性中立型阻尼微分方程的振动性与渐近性
Oscillatory and asymptotic behavior of a class of even order nonlinear neutral damped functional differential equations
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摘要: 考虑以下偶数阶非线性中立型阻尼微分方程的振动性与渐近性:x(t)+ (t)x(τi(t))(n)+b(t)x(t)+ (t)x(τi(t))(n-1)+q(t)f(x(σ(t)))=0,t≥t0,获得了该类方程所有解振动的2个准则,推广了现有文献的一些结果.此外,还获得了关于该类方程每一个有界解的振动性与渐近性的2个充分条件.Abstract: It is considered that the oscillation and asymptotic behavior of the following even order nonlinear neutral damped functional differential equationsx(t)+ (t)x(τi(t))(n)+b(t)x(t)+ (t)x(τi(t))(n-1)+q(t)f(x(σ(t)))=0,t≥t0,two criteria for the oscillation of all its solutions are obtained,which extend some known results in the literature.Furthermore,two sufficient conditions for the oscillation and asymptotic behavior of every bounded solution are presented.