Oscillation of odd order neutral delay differential equation. (English) Zbl 0837.34070

Das, P.

Czech. Math. J. 45, No. 2, 241-251 (1995).

The author considers neutral delay differential equations in the form \[ Nx (t) : = \left( x(t) - \sum^K_{j = 1} p_j x(t - \tau_j) \right)^{(n)} = - \sum^m_{i = 1} Q_i (t) x(t - \sigma_i), \tag{1} \]
\[ Nx(t) = - \sum^m_{i = 1} Q_i (t)f_i \bigl( x(t - \sigma_i) \bigr), \tag{2} \] where \(n\) is odd, \(p_j\), \(\tau_j > 0\) \((j = 1, \dots, K)\); \(\sigma_i > 0\), \(Q_i \in C ([a, \infty), (0, \infty))\), \(f_i \in C (R,R)\), \(xf_i (x) > 0\) for \(x \neq 0\) \((i = 1, \dots, m)\), \(\sum^m_{j = 1} p_j < 1\). There are proved sufficient conditions under which all solutions of (1), (2) are oscillatory.

Reviewer: P.Marušiak (Žilina)

MSC:

34K11	Oscillation theory of functional-differential equations
34C10	Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34C11	Growth and boundedness of solutions to ordinary differential equations
34K40	Neutral functional-differential equations

Keywords:

neutral delay differential equations; oscillatory

References:

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