In this paper, based on the Lyapunov-Krasovskii functional approach, we obtain sufficient conditions which guarantee stability, uniformly stability, boundedness and uniformly boundedness of solutions of certain third order non- autonomous differential equations of retarded type. Our results complement and improve some recent ones.

/pdf/on-the-stability-and-boundedness-of-certain-third-order-non-1s99ieell6.pdf

On the stability and boundedness of certain third order non-autonomous differential equations of retarded type

In this paper, some new conditions on the global asymptotic stability, boundedness and ultimate boundedness of solutions to a certain fourth order nonlinear differential equation are obtained. By constructing a complete Lyapunov function, we give three new results on the considered equation. Our results improve, generalize and complement existing results in the literature on the subject matter.

Some new stability and boundedness results on a certain fourth order nonlinear differential equation

In this paper, we give sufficient conditions to guarantee the asymptotic
 stability and boundedness of solutions to a kind of fourth-order functional
 differential equations with multiple delays. By using the Lyapunov-Krasovskii
 functional approach, we establish two new results on the stability and
 boundedness of solutions, which include and improve some related results in
 the literature.

/pdf/stability-and-boundedness-to-certain-differential-equations-8nyt3m7thu.pdf

Stability and boundedness to certain differential equations of fourth order with multiple delays

In this paper, sufficient criteria which guarantee the existence of uniform asymptotic stability and boundedness of solution of a scalar real fourth-order delay differential equation were established with the aid of a suitable Lyapunov function. With the Lyapunov function, conditions on the nonlinear terms to guarantee stability and boundedness of the solution and its derivatives were given. Our results include and improve on the existing results in the literature.

On stability and boundedness of solutions of certain fourth order delay differential equation

In this paper, we give sufficient conditions to guarantee the asymptotic stability and boundedness of solutions to a kind of fourth-order functional differential equations with multiple retardations. By using the LyapunovKrasovskii functional approach, we establish two new results on the stability and boundedness of solutions, which include and improve some related results in the literature.

/pdf/on-some-qualitative-behaviors-of-certain-differential-328zp63myk.pdf

On some qualitative behaviors of certain differential equations of fourth order with multiple retardations

Department of Pure and Applied Mathematics, University of Fort Hare,Alice, 5700, RSA.E-mail: Gokecha@ufh.ac.zaAbstract We give sucient conditions for the existence of a stable (globally asymp-totically stable), bounded and uniform ultimate bounded solution to a certain fourthorder non-linear di erential equation using a single complete Lyapunov function with-out the use of a signum function or any stringent condition on the nonlinear terms.Theresults include and improve some existing results in literature.

Boundedness and stability properties of solution to certain fourth order non-linear differential equation

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Boundedness and stability properties of solution to certain fourth order non-linear differential equation