On the stability and boundedness of a class of higher order delay differential equations

Tunç, Cemil

doi:10.1016/j.jfranklin.2010.04.006

Cited by 3 publications

(1 citation statement)

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“…In particular, there have been extensive results on the boundedness of solutions of various nonlinear differential equations of second order in the literature. For example, for a comprehensive treatment of the subject on the boundedness of solutions, we refer the readers to books of Ahmad and Rama Mohana Rao [1], Krasovskii [11], Yoshizawa [22] and the papers of Graef [3,4], Graef and Spikes [5,6,7], Huang et al [9], Jin [10], Murakami [12], Saker [13], Sun [14], Tunç [15,16,17], Tunç and Şevli [18], Tunç and Tunç [19], Villari [20], Ye et al [21], Zhao [24], Waltman [25], Wong [26], Wong and Burton [27] and the references contained in these sources. Thus, it is worthwhile to continue to the investigation of the boundedness of solutions of nonlinear differential equations of second order in this case.…”

Section: Introductionmentioning

confidence: 99%

Boundedness Results for Solutions of Certain Nonlinear Differential Equations of Second Order

Tunç

2012

JIMS

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Abstract. In this paper, we establish some new sufficient conditions which guarantee the boundedness and the uniform boundedness of solutions of certain nonlinear and nonautonomous differential equations of second order. By defining appropriate Liapunov functions, we obtain some new results on the subject, and examples are also provided to illustrate the feasibility of the proposed results. By this work, we extend and improve some boundedness results in the literature.Key words and Phrases: Nonautonomous, differential equation, second order; boundedness, uniform boundedness.Abstrak. Dalam paper ini, kami membangun syarat cukup baru yang menjamin keterbatasan dan keterbatasan seragam dari solusi suatu persamaan differensial nonlinier tertentu dan nonautonomus derajat dua. Dengan mendefinisikan fungsi Liapunov, kami memperoleh suatu hasil baru dalam topik tersebut dan contoh-contoh diberikan untuk memberikan ilustrasi dari fisibilitas hasil yag diusulkan. Dengan penelitian ini, kami memperluas dan memperbaiki hasil-hasil dalam kajian keterbatasan.Kata kunci: Nonautonomus, persamaan diferensial, derajat dua, keterbatasan, keterbatasan seragam.

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