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Oscillation criteria for a class of third-order nonlinear neutral differential equations

Zhong J., Ouyang Z., Zou S.

Journal of Applied Analysis

2011

Vol. 17, nr 2

155-163

A class of third-order nonlinear neutral differential equation (r(t)(y"(t)) α)' + q(t) f(x(σ (t))) = 0 is investigated in this paper, where y(t) = x(t) + p(t)x(?(t)), and ? > 0 is any quotient of odd integers. Using a new method, we obtain some sufficient conditions for the oscillation of the above equation, and some known oscillation criteria be extended. An example is inserted to illustrate the result.

On two second order half-linear difference equations

Zhang G., Cheng S. S.

Fasciculi Mathematici

2005

Nr 35

163-175

In this paper, two second order half-linear difference equations are considered. By establishing their connections with a standard half-linear difference equation, we are able to obtain sufficient conditions for existence and nonexistence of eventually positive solutions.