A Boundedness Theorem for a Certain Third Order Nonlinear Differential Equation

Boundedness of Solutions of a Third-order Nonlinear Differential Equation

Sufficient conditions are established for the boundedness of all solutions of (1.1), and we also present some sufficient conditions, which ensure that the limits of first and second order derivatives of the solutions of (1.1) tend to zero as t→∞. Our results improve and include those results obtained by previous authors ([3], [5]).

Nonlinear oscillation of certain third-order neutral differential equation with distributed delay

The authors obtain necessary and sufficient conditions for the existence of oscillatory solutions with a specified asymptotic behavior of solutions to a nonlinear neutral differential equation with distributed delay of third order. We give new theorems which ensure that every solution to be either oscillatory or converges to zero asymptotically. Examples dwelling upon the importance of applicab...

Some New Results on the Boundedness of Solutions of a Certain Nonlinear Differential Equation of Third Order

In this paper, the boundedness of solutions of a third-order nonlinear differential equation is investigated. Some criteria on the regularity and asymptotic behavior of solutions for the same equation are also given. The obtained results are further extensions that of Mehri&Shadman [1], and also include the theorems established there.

ON TE EXISTENCE OF PERIODIC SOLUTION FOR CERTAIN NONLINEAR THIRD ORDER DIFFERENTIAL EQUATIONS

New Result in the Ultimate Boundedness of Solutions of a Third-order Nonlinear Ordinary Differential Equation

Sufficient conditions are established for the ultimate boundedness of solutions of certain third-order nonlinear differential equations. Our result improves on Tunc’s [C. Tunc, Boundedness of solutions of a third-order nonlinear differential equation, J. Inequal. Pure and Appl. Math., 6(1) Art. 3,2005,1-6].