On the Convergence of Solutions of Certain Third-Order Differential Equations

On the Convergence of Solutions of Certain Third-Order Differential Equations

As well known, in the investigation of qualitative behaviors of solutions, stability, convergence, boundedness, oscillation, and so forth of solutions are very important problems in theory and applications of differential equations. For example, in applied sciences, some practical problems concerning mechanics, the engineering technique fields, economy, control theory, physics, chemistry, biolo...

Convergence of Solutions of Certain Fourth-Order Nonlinear Differential Equations

We give sufficient criteria for the existence of convergence of solutions for a certain class of fourth-order nonlinear differential equations using Lyapunov's second method. A complete Lyapunov function is employed in this work which makes the results to include and improve some existing results in literature. This is an open access article distributed under the Creative Commons Attribution Li...

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

On the Stability of Solutions of Certain Non-Linear Third-Order Delay Differential Equations

In this paper, we study equation (1.6) and (1.7) and establish some sufficient conditions for the asymptotic stability of the zero solution of them.

On the Asymptotic Behavior of Solutions of Certain Third-order Nonlinear Differential Equations

where ψ ∈ C(R×R×R,R), f ∈ C(R×R,R), and p ∈ C([0,∞)×R×R×R,R). It is also supposed that the functions ψ, f , and p depend only on the arguments displayed explicitly, and the dots denote differentiation with respect to t. However, we shall require that f (0,0) = 0, the derivatives ∂ψ(x, ẋ, ẍ)/∂x ≡ ψx(x, ẋ, ẍ), ∂ψ(x, ẋ, ẍ)/∂ẍ ≡ ψẍ(x, ẋ, ẍ), and ∂ f (x, ẋ)/∂x ≡ fx(x, ẋ) exist and are continuous, an...