ON THE UNIFORM DISSIPATIVITY OF SOME FIFTH-ORDER NON-LINEAR DIFFERENTIAL EQUATIONS

This paper studies the problem of uniformly dissipative solutions of somefifth order non-linear differential equations by the use of frequency domaintechnique. We use the generalized theorem of Yacubovich on dissipativity toobtain some new sufficient conditions of the existence of solutions that aredissipative for (1.1) and (1.2).     

Remarks on Barbashin-Ezeilo Problem on third-order nonlinear differential equations

In this paper, we use the frequency domain criteria to initiate a general result on the Barbashin-Ezeilo Problem on third-order nonlinear differential equation. Earlier ideas of Burkin [I.M. Burkin, Orbital stability of second-kind limiting cycles for dynamical systems with cylindrical phase space, Differential Equations 29 (1993) 1262-1264], Leonov [G.A. Leonov, A frequency criterion for the existence of limit cycles of dynamical systems with cylindrical phase spaces, Differential Equations 23 (1987) 1375-1378] on the problem are being improved upon.     

On the stability and boundedness of solutions of a kind of third order delay differential equations

In this paper, we study Eq. (1.1) for asymptotic stability of the zero solution when and uniformly bounded and uniformly ultimate bounded of all solutions when      

Ultimate boundedness results for a certain system of third-order non-linear differential equations

We present in this paper ultimate boundedness results for a third-order system of non-linear differential equations of the form $\text{·X + A}\text{X}\text{?}\text{+ B/.X + H(X) = P(t, X, /.X,}\text{X}\text{?}\text{)}$. where A, B are constant symmetric n × n matrices and X, H(X), P(t, X, X, X) are real n-vectors with H:R_n→R_n and P: RXR_nXR_nXR_nXR_n → XR_ncontinuous in their respective arguments. Our results give an n-dimensional analogue of an earlier result of Ezeilo in [1] and extend other earlier results for the case in which we do not necessarily require that H(X) be differentiable.     

CONVERGENCE OF SOLUTIONS OF CERTAIN SYSTEM OF THIRD ORDER NON-LINEAR ORDINARY DIFFERENTIAL EQUATIONS

The object of this paper is to give an n-dimensional analogue of a convergence result of Tejumola [8] for some third-order differential equations. The result extends earlier results of Afuwape [1] and Ezeilo [4] to some system of third-order differential equations.     

On the Applications of the Frequency-Domain Method for Uniformly Dissipative Non-Linear Systems

In this paper, we introduce the idea of dual systems of the frequency-domain method for uniform dissipativity. We prove the equivalence of the frequency-domain conditions for dual systems and apply it to a third-order non-linear differential equation arising from the vacuum tube circuit problem studied by Rauch [8]. An earlier result of BARBALAT and HALANAY [5] is obtained as a particular case.