On oscillation criteria for forced nonlinear higher order neutral differential equations

Rok, strany: 2004, 369 - 388

In this paper, sufficient conditions are obtained for oscillation of all solutions of neutral differential equations of the form

$$ [y(t)-p(t)y(t-τ)]⁽ⁿ⁾ +∑\limits_i=1^m Q_i(t)G(y(t-σ_i)) =f(t) \tag"$(*)$" $$

and

$$ [{y(t) - p(t)y({t - τ})}]⁽ⁿ⁾ +∑\limits_i=1^m Q_i(t)G(y(t-σ_i)) =0 \tag"$(**)$" $$

for different ranges of $p(t)$, where $n ≥ 2$. For $(*)$, one of the conditions states that $F(t)$ changes sign finitely, where $F \in C⁽ⁿ⁾([0,∞), \Bbb R )$ with $F⁽ⁿ⁾(t) = f(t)$. In results concerning $(**)$, the nonlinearity of $G$, the nature of $n$ and the range of $p(t)$ are closely related.

ISO 690:

Parhi, N., Rath, R. 2004. On oscillation criteria for forced nonlinear higher order neutral differential equations. In Mathematica Slovaca, vol. 54, no.4, pp. 369-388. 0139-9918.

APA:

Parhi, N., Rath, R. (2004). On oscillation criteria for forced nonlinear higher order neutral differential equations. Mathematica Slovaca, 54(4), 369-388. 0139-9918.