We establish sufficient conditions under which all solutions of the third-order nonlinear differential equation x + ψ ( x , x ˙ , x ¨ ) x ¨ + f ( x , x ˙ ) = p ( t , x , x ˙ , x ¨ ) are bounded and converge to zero as t → ∞ .

https://downloads.hindawi.com/archive/2005/283676.pdf

On the asymptotic behavior of solutions of certain third-order nonlinear differential equations

Boundedness results for a certain third order nonlinear differential equation

(1.2) x+a(t)f(x, Λ, x)x+b(t)g(x9 x)+c(t)h(x) = p(t, x, i, x) where a(t), b(t)y c(t) are positive continuously differentiate and /, g, h, p are continuous real-valued functions depending only on the arguments shown, and the dots indicate the differentiation with respect to t. The asymptotic property of solutions of third order differential equations has received a considerable amount of attention during the past two decades, particularly when (1.2) is autonomous. Many of these results are summarized in [11]. A few authors have studied non-autonomous third order differential equations. K. E. Swick [13] considered the following equations

/pdf/on-the-asymptotic-behavior-of-solutions-of-certain-non-a58nzqz8h7.pdf

On the asymptotic behavior of solutions of certain non-autonomous differential equations

We establish some new sufficient conditions to the uniform asymptotically stability and boundedness of the solutions for a kind of non-autonomous differential equations of third order with constant delay. By defining an appropriate Lyapunov functional, we prove two new theorems on the subject. Our results improve and form a complement to some known recent results in the literature.

/pdf/stability-and-boundedness-for-a-kind-of-non-autonomous-28xx5ow0je.pdf

Stability and boundedness for a kind of non-autonomous differential equations with constant delay

We consider a nonautonomous functional differential equation of the third order with multiple deviating arguments. Using the Lyapunov-Krasovskii functional approach, we give certain sufficient conditions to guarantee the asymptotic stability and uniform boundedness of the solutions.

/pdf/stability-and-uniform-boundedness-in-multidelay-functional-wspeyytulo.pdf

K. E. Swick

Papers

Asymptotic Behavior of the Solutions of Certain Third Order Differential Equations