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This paper considers a non-autonomous differential equation of second order with multiple variable deviating arguments. By using time-varying delay Lyapunov-Krasovskii functional, we propose to find some sufficient conditions for the solutions of the equation considered are quadratic integrable. [ABSTRACT FROM AUTHOR]

This paper considers a non-autonomous differential equation of second order with multiple variable deviating arguments. By using time-varying delay Lyapunov-Krasovskii functional, we propose to find some sufficient conditions for the solutions of the equation considered are quadratic integrable. [ABSTRACT FROM AUTHOR]

This paper establishes some new sufficient conditions to ensure the stability and boundedness of solutions of certain second order non-autonomous and non-linear differential equations. By defining two appropriate Liapunov functions, we obtain three new results on the subject and give some examples to illustrate the theoretical analysis in this work. By this work, as well as two new results, we also extend and improve an important result from the literature. [ABSTRACT FROM AUTHOR]

We establish some new sufficient conditions which guarantee the boundedness and the uniform ultimate boundedness of the solutions of a kind of nonlinear differential equations of third order. By defining an appropriate Lyapunov function, we prove two new theorems on the subject. Our results generalize and are complement some known boundedness results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we consider a nonlinear differential equation of third order. By the Lyapunov function approach, we discuss the convergence of the solutions of the equation considered. Our findings generalize some well known results in the literature. [ABSTRACT FROM AUTHOR]

This paper presents sufficient conditions for all solutions as well as their derivatives up to second order to x‴ +a(t)f (x′)x″ + b(t, x, x′)+c(t)g(x) = e(t, x, x′, x″) to be bounded. What is more, it shows that all the solutions are in LP[0, ∞) under somewhat more restrictive conditions. [ABSTRACT FROM AUTHOR]

This paper presents sufficient conditions for all solutions as well as their derivatives up to second order to x‴+a(t)f(x′)x″+b(t, x, x′)+c(t)g(x) = e(t, x, x′ , x″) to be bounded. What is more, it shows that all the solutions are in Lp[0,∞) under somewhat more restrictive conditions. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the existence of periodic solutions to nonlinear third order delay differential equation: x‴(t) +ψ (x′(t))x″(t) + g(x′(t - r)) + f (x(t)) = p(t, x(t), x(t - r), x′(t), x′(t - r), x″(t)), when p(t, x(t), x(t - r), x′(t), x′(t - r), x″(t)) is a periodic function of period T , T > 0. With use of Lyapunov's functional approach, we establish some new sufficient conditions which guarantee that there exists a periodic solution of this equation of period T , T > 0. For illustrations, an example is also given on the existence of periodic solutions. [ABSTRACT FROM AUTHOR]