Oscillation theorems for certain even order neutral differential equations

Yang, Qi Gui ; Cheng, Sui-Sun

Archivum Mathematicum, Tome 043 (2007), p. 105-122 / Harvested from Czech Digital Mathematics Library

Résumé

This paper is concerned with a class of even order nonlinear differential equations of the form \[ \frac{d}{dt}\Big ( \Big |\left( x(t)+p(t)x(\tau (t))\right) ^{(n-1)}\Big | ^{\alpha -1}(x(t)+p(t)x(\tau (t)))^{(n-1)}\Big ) +F\big ( t,x(g(t))\big ) =0\,, \] where $n$ is even and $t\ge t_{0}$. By using the generalized Riccati transformation and the averaging technique, new oscillation criteria are obtained which are either extensions of or complementary to a number of existing results. Our results are more general and sharper than some previous results even for second order equations.

Détail

Publié le : 2007-01-01

MR 2336963 | Zbl 1164.34031

Classification:  34K11

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