Stability and ultimate boundedness of solutions of some third order differential equations with delay

Abstract

This paper is devoted to study the boundedness, ultimate boundedness, and the asymptotic stability of solutions for a certain class of third-order nonlinear differential equations using Lyapunov's second method. Our results improve and form a complement to some earlier results in the literature.

Asymptotic stability for third-order non-homogeneous differential-operator equations

“…For more detailed physical interpretation, existence, and uniqueness of the solutions, we refer to [10]. It can be stated that (3.1) differs from the equation for acoustic waves in uniform medium only by the fact that the coefficients are not constant.…”

“…It is shown under some conditions, compatible with the Routh-Hurwitz criterion, that the solution of the equation is asymptotically stable, and that every solution of the equation tends to zero with an exponential rate. For other studies on stability in the third-order problems, one can see [8][9][10][11][12].…”

Continuability and boundedness of solutions to a differential equation of third order with multiple deviating arguments

“…[9], Ademola vd. [10], Ademola [11], Ayhan [12], Ayhan ve Sofuoglu [13], Remili ve Oudjedi [14][15], Remili ve Beldjerd [16], Tunç ve Ayhan [17][18][19][20], Tunç [21] ve bu çalışmada atıfta bulunulan diğer çalışmalar incelenebilir. Bu çerçevede son zamanlarda Remili ve Beldjerd [16] tarafından ( ) > 0 olmak üzere ( ( ) ′ ) ′′ + ( ) ( ′ ) ′′ + ( ) ( ′ ) + ( )ℎ( ( − ( )) = ( , ( ), ( − ( ), ′ ( − ( ), ′′ ( ))…”

Stability of the solutions of nonlinear third order differential equations with multiple deviating arguments

“…Many interesting results, on the qualitative behavior of solutions of the third order differential equations have been obtained by Omeike [4,5], Remili and Oudjedi [7], Sadek [8,9], Tunç [11,12,13,14] and Zhu [17] and references therein.…”