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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 the bounds for mean-values of solutions to certain third-order non-linear differential equations

Afuwape A. U., Adesina O. A.

Fasciculi Mathematici

2005

Nr 36

5-14

In this paper, the issue of bounds for the mean-values of solutions of some third-order differential equations with non-linear terms is considered. It is shown that these bounds are independent of the solutions for the considered equations.