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On the oscillation of third-order quasi-linear neutral functional differential equations

Ethiraju Thandapani, Tongxing Li (2011)

Archivum Mathematicum

The aim of this paper is to study asymptotic properties of the third-order quasi-linear neutral functional differential equation [ a ( t ) ( [ x ( t ) + p ( t ) x ( δ ( t ) ) ] ' ' ) α ] ' + q ( t ) x α ( τ ( t ) ) = 0 , E where α > 0 , 0 p ( t ) p 0 < and δ ( t ) t . By using Riccati transformation, we establish some sufficient conditions which ensure that every solution of () is either oscillatory or converges to zero. These results improve some known results in the literature. Two examples are given to illustrate the main results.

On the oscillatory integration of some ordinary differential equations

Octavian G. Mustafa (2008)

Archivum Mathematicum

Conditions are given for a class of nonlinear ordinary differential equations x ' ' + a ( t ) w ( x ) = 0 , t t 0 1 , which includes the linear equation to possess solutions x ( t ) with prescribed oblique asymptote that have an oscillatory pseudo-wronskian x ' ( t ) - x ( t ) t .

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