On the stability of solutions of nonlinear differential equations of fifth order with delay

Criteria for global asymptotic stability of a null solution of a nonlinear differential equation of fifth order with delay% begin{eqnarray*} &&x^{(5)}(t)+psi (x(t-r),x^{prime }(t-r),x^{prime prime }(t-r),x^{prime prime prime }(t-r),x^{(4)}(t-r))x^{(4)}(t) \ &&quad+f(x^{prime prime }(t-r),x^{prime prime prime }(t-r))+alpha _{3}x^{prime prime }(t)+alpha _{4}x^{prime }(t)+alpha _{5}x(t)=0 end{eqnarray*} are obtained by using Lyapunov\u27s second method. By defining a Lyapunov functional, sufficient conditions are established, which guarantee the null solution of this equation is globally asymptotically stable. Our result consists of a new theorem on the subject

Qualitative properties in nonlinear Volterra integro-differential equations with delay

AbstractThis paper considers a class of scalar and vector nonlinear Volterra integro-differential equations of the first order with a constant delay. We demonstrate the stability, uniform stability, boundedness, convergence and square integrability of the solutions. The technique of proof involves defining appropriate Lyapunov functionals. Our results improve the results obtained in the literature

A Further Result on the Instability of Solutions to a Class of Non-Autonomous Ordinary Differential Equations of Sixth Order

The aim of the present paper is to establish a new result, which guarantees the instability of zero solution to a certain class of non-autonomous ordinary differential equations of sixth order. Our result includes and improves some well-known results in the literature

Unstable Solutions to Nonlinear Vector Differential Equations of Sixth Order with Delay

This paper investigates the instability of the zero solution of a certain vector differential equation of the sixth order with delay. Using the Lyapunov- Krasovskiĭ functional approach, we obtain a new result on the topic and give an example for the related illustration

On the qualitative behaviors of a functional differential equation of second order

The aim of this paper is first to investigate the stability of the zero solution to a new Liénard type equation with multiple variable delays by two different methods. The methods to be used in the proofs involve the Lyapunov-Krasovskiĭ functional approach and the fixed point technique under an exponentially weighted metric, respectively. We make a comparison between the applications of these methods with the established conditions on the same stability problems. Then, we obtain three new results for uniformly stability and boundedness/ uniformly boundedness of the solutions to the considered equation by the Lyapunov-Krasovskiĭ functional approach. An example is given to verify the results obtained by the Lyapunov-Krasovskiĭ functional approach. Our results complement and improve some recent ones in the literature

(R1897) Further Results on the Admissibility of Singular Systems with Delays

Admissibility problem for a kind of singular systems with delays is studied in this article. Firstly, given the singular system with delays is transformed into a neutral system with delays. Secondly, a new sufficient criterion is obtained on the stability of the new neutral system by aid of Wirtinger-based integral inequality, linear matrix inequality (LMI) method and meaningful Lyapunov-Krasovskii functionals (LKFs). This criterion is valid for both systems. At the end, Two numerical examples are given to illustrate the applicability of the obtained results using MATLAB-Simulink software. By this article, we extend and improve some results of the past literature

Boundedness of Solutions to Differential Equations of Fourth Order with Oscillatory Restoring and Forcing Terms

This paper deals with the boundedness of solutions to a nonlinear differential equation of fourth order. Using the Cauchy formula for the particular solution of nonhomogeneous differential equations with constant coefficients, we prove that the solution and its derivatives up to order three are bounded

On the Global Existence and Boundedness of Solutions of Nonlinear Vector Differential Equations of Third Order

In this paper, we give some criteria to ensure the global existence and boundedness of solutions to a kind of third order nonlinear vector differential equations. By using the Lyapunov\u27s direct method, we obtain a new result on the topic and give an example for the illustrations. Our result includes, completes and improves some earlier results in the literature

On the Asymptotic Stability of a Nonlinear Fractional-order System with Multiple Variable Delays

In this paper, we consider a nonlinear differential system of fractional-order with multiple variable delays. We investigate asymptotic stability of zero solution of the considered system. We prove a new result, which includes sufficient conditions, on the subject by means of a suitable Lyapunov functional. An example with numerical simulation of its solutions is given to illustrate that the proposed method is flexible and efficient in terms of computation and to demonstrate the feasibility of established conditions by MATLAB-Simulink

Stability and Uniform Boundedness in Multidelay Functional Differential Equations of Third Order

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