2010
DOI: 10.1590/s1807-03022010000300001
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Abstract: Abstract. This paper studies the stability and boundedness of solutions of certain nonlinear third-order delay differential equations. Sufficient conditions for the stability and boundedness of solutions for the equations considered are obtained by constructing a Lyapunov functional.Mathematical subject classification: 34K20.

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Cited by 14 publications
(8 citation statements)
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“…It follows that the equation (12) is a special case of (1.4). Our purpose is to extend and improve the result established by [4] and [23,21,30] for the asymptotic stability of the null solution and boundedness of all solutions, when p = 0 and p = 0 in (1.4). By defining an appropriate Lyapunov functional we show similar results for nonlinear equations (1.3) and (1.4).…”
Section: Introductionmentioning
confidence: 89%
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“…It follows that the equation (12) is a special case of (1.4). Our purpose is to extend and improve the result established by [4] and [23,21,30] for the asymptotic stability of the null solution and boundedness of all solutions, when p = 0 and p = 0 in (1.4). By defining an appropriate Lyapunov functional we show similar results for nonlinear equations (1.3) and (1.4).…”
Section: Introductionmentioning
confidence: 89%
“…In particular, there have been extensive results on the stability and boundedness of solutions of various nonlinear differential equations of third order in the literature. See for instance the papers of Ademola [1,2], Afuwape and Omeike [3], Oudjedi et al [15], Remili et al [16,17], Tunç [16][17][18][19][20], Zhu [34] and the references contained in these sources.…”
Section: Introductionmentioning
confidence: 99%
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“…In the last years, there is a good amount of interest in the qualitative behaviors of ordinary and functional differential equations of third order without and with delay, see the book of Reissig et al [1] as a good survey for the works done by 1974 and the papers of Ademola and Arawomo ( [2], [3], [4], [5]), Ademola et al [6], Afuwape and Castellanos [7], Afuwape and Omeike [8], Ahmad and Rama Mohana Rao [9], Bai and Guo [10], Ezeilo [11], Ezeilo and Tejumola [12], Graef et al ([13], [14]), Graef and Tunc [15], Korkmaz and Tunc [16], Mahmoud and Tunc [17], Ogundare [18], Ogundare et al [19], Olutimo [20], Omeike [21], Qian [22], Remili and Oudjedi [23], Sadek [24], Swick [25], Tejumola and Tchegnani [26], Tunc ([27]- [44]), Tunc and Ates [45], Tunc and Gozen [46], Tunc and Mohammed [47], Tunc and Tunc [48], Zhang and Yu [49], Zhu [50] and theirs references. However, to the best of our knowledge from the literature, by this time, no attention was given to the investigation of the globally asymptotic stability/uniformly stability, boundedness and uniformly boundedness in the systems of nonlinear functional differential equations of third order with variable delay, except the recent work of Omeike [21].…”
Section: Introductionmentioning
confidence: 99%