Cemil Tunç

On the asymptotic behavior of solutions of certain second-order differential equations

Abstract In this paper, the second order non-linear differential equation x ¨ + a ( t ) f ( x , x ˙ ) x ˙ + b ( t ) g ( x ) = p ( t , x , x ˙ ) is considered, and Lyapunovs second method is used to show that uniform boundedness and convergence to zero of all solutions of this equation together with their derivatives of the first order.

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

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 → ∞ .

Pseudo almost periodic solutions for CNNs with leakage delays and complex deviating arguments

In this paper, cellular neural networks with leakage delays and complex deviating arguments are considered. Some criteria are established for the existence of pseudo almost periodic solutions for this model by using the exponential dichotomy theory, contraction mapping fixed point theorem and inequality analysis technique. The results of this paper are new and complement previously known results.

An instability result for certain system of sixth order differential equations

The main purpose of this paper is to give sufficient conditions for the instability of the trivial solution X=0 of Eq. (1.1).

Bound of solutions to third-order nonlinear differential equations with bounded delay

Abstract A theorem is presented that contains some sufficient conditions to ensure bound of solutions to a third-order nonlinear delay differential equation. It is shown that this theorem improves the result of Ponzo [On the stability of certain nonlinear differential equations, IEEE Trans. Automatic Control AC-10 (1965) 470–472] to the bound of solutions for the equation considered.

BOUNDEDNESS AND STABILITY PROPERTIES OF SOLUTIONS OF CERTAIN FOURTH ORDER DIFFERENTIAL EQUATIONS VIA THE INTRINSIC METHOD

Received: May 25, 1994; r ev i sed : December 23, 1995 Abstract :In this paper, firstly a Lyapunov function is derived for (1.2) by applying the intrinsic method introduced by Chin[6], Secondly equation (1.2) is examined in two cases : (i) Ρ s 0, (ii) Ρ * 0 . For case (i) the asymptotic stability in the large of the trivial solution χ = 0 is investigated and for case (ii) the boundedness results are obtained for solutions of equation (1.2). These results improve and include several well-known results. AMS Classification numbers: 34D20, 34D99.

On the qualitative behaviors of solutions of some differential equations of higher order with multiple deviating arguments

Abstract We study the boundedness of the solutions to a non-autonomous and non-linear differential equation of second order with two constant deviating arguments. We give two examples to illustrate the main results. By this work, we extend some boundedness results obtained for a differential equation with a constant deviating argument in the literature to the boundedness of the solutions of a differential equation with two constant deviating arguments.

A New Instability Result to Nonlinear Vector Differential Equations of Fifth Order

By constructing a Lyapunov function, a new instability result is established, which guarantees that the trivial solution of a certain nonlinear vector differential equation of the fifth order is unstable. An example is also given to illustrate the importance of the result obtained. By this way, our findings improve an instability result related to a scalar differential equation in the literature to instability of the trivial solution to the afore-mentioned differential equation.

Some remarks on the stability and boundedness of solutions of certain differential equations of fourth-order

There are given sufficient conditions for the asymptotic stability of the zero solution of equation (1.1) with p = 0 and the boundedness of all solutions of the same equation (1.1), with p ¹ 0.

On the boundedness and periodicity of the solutions of a certain vector differential equation of third-order

There are given sufficient conditions for the ultimate boundedness of solutions and for the existence of periodic solutions of a certain vector differential equation of third-order.