Geodesic
Oscillation theorems for certain even order neutral differential equations
Archivum mathematicum, Tome 43 (2007) no. 2, pp. 105-122 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 34K11
Keywords: neutral differential equation; oscillation criterion; Riccati transform; averaging method 
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Yang, Qi Gui; Cheng, Sui-Sun. Oscillation theorems for certain even order neutral differential equations. Archivum mathematicum, Tome 43 (2007) no. 2, pp. 105-122. http://geodesic.mathdoc.fr/item/ARM_2007_43_2_a2/

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