Oscillatory and asymptotic behavior of a class of even order nonlinear neutral damped functional differential equations. (Chinese. English summary) Zbl 1174.34053
Summary: Consider the oscillation and asymptotic behavior of the following even order nonlinear neutral damped functional differential equation
\[
[x(t)+\sum^h_{i=1}p_i(t)x(\tau_i(t))]^{(n)}+b(t)[x(t)+\sum^h_{i=1}p_i(t)x(\tau_i(t))]^{(n-1)}+q(t)f(x(\sigma(t)))=0,\;t\geqslant t_0.
\]
Two criteria for the oscillation of all its solutions are obtained. Furthermore, two sufficient conditions for the oscillation and asymptotic behavior of every bounded solution are presented.
MSC:
34K11 | Oscillation theory of functional-differential equations |
34K40 | Neutral functional-differential equations |
34K25 | Asymptotic theory of functional-differential equations |