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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