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On asymptotic behaviors of solutions of “almost linear” and essential nonlinear functional differential equations

✍ Scribed by Roman Koplatadze

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
225 KB
Volume
71
Category
Article
ISSN
0362-546X

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✦ Synopsis

In the paper the following differential equation

We say that the equation is ''almost linear'' if the condition lim t→+∞ µ(t) = 1 is fulfilled, while if there exists λ ∈ (0, 1) (λ ∈ (1, +∞)) such that µ(t) ≤ λ (µ(t) ≥ λ), then we say that the equation is an essentially nonlinear differential equation.

''Almost linear'' and essentially nonlinear differential equations are considered and sufficient (necessary and sufficient) conditions for the equation to have Property B are established.

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On the qualitative behaviors of solutions of third-order nonlinear functional differential equations
✍ Mustafa Fahri Aktaş; Devrim Çakmak; Aydın Tiryaki 📂 Article 📅 2011 🏛 Elsevier Science 🌐 English ⚖ 263 KB

The third-order nonlinear functional differential equations of the form are considered. We present some new oscillatory and asymptotic behavior of solutions of this equation by modifying a method given for second-order differential equations. Our results are applicable to nonlinear functional diffe