Meromorphic solutions of a 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...

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].

Existence of positive solutions of a third order nonlinear differential equation with positive and negative terms

Existence of Nonoscillatory Solutions for a Third-Order Nonlinear Neutral Delay Differential Equation

and Applied Analysis 3 Throughout this paper, we assume that R −∞, ∞ , R 0, ∞ , C t0, ∞ ,R denotes the Banach space of all continuous and bounded functions on t0, ∞ with the norm ‖x‖ supt≥t0 |x t | for each x ∈ C t0, ∞ ,R and A N,M {x ∈ C t0, ∞ ,R : N ≤ x t ≤ M, t ≥ t0} for M > N > 0. 1.8 It is easy to see that A N,M is a bounded closed and convex subset of C t0, ∞ ,R . By a solution of 1.7 , w...