Linear functional differential equations with Property A

In this paper, an nth order functional differential equation is considered for which the generalized Emden-Fowler-type equationcan be considered as a nonlinear model. Here, we assume that n 2, p ∈ L loc (R + ; R), and µ ∈ C(R + ; (0, 1]) is a nondecreasing function. In case µ(t) ≡ const > 0, oscillatory properties of Eq. (0.1) have been extensively studied, where as if µ(t) / ≡ const, to the extent of authors' knowledge, the analogous questions have not been examined. It turns out that the oscillatory properties of Eq. (0.1) substantially depend on the rate at which the function µ + − µ(t) tends to zero as t → +∞, where µ + = lim t→+∞ µ(t). In this paper, new sufficient conditions for a general class of nonlinear functional differential equations to have Properties A and B are established, and these results apply to the special case of Eq. (0.1) as well.  2005 Elsevier Inc. All rights reserved.

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“…The proof of the lemma in the case where u (n) (t) 0 can be found in [14]. The case where u (n) (t) 0 can be proved analogously.…”

Section: )mentioning

confidence: 95%

Nonlinear functional differential equations with Properties A and B

Graef

Koplatadze

Kvinikadze

2005

Journal of Mathematical Analysis and Applications

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“…When m = 1 and η 1 (t) ≡ 1, Eq. (1.4) is a linear ordinary differential equation whose oscillatory properties are studied in [1][2][3][4][5] well enough. When m = 1 and η 1 (t) ≡ η > 0, η = 1, (1.4) becomes the essentially nonlinear ordinary differential equation of Emden-Fowler type.…”

Section: Introductionmentioning

confidence: 99%

Quasi-linear functional differential equations with Property A

Koplatadze¹

2007

Journal of Mathematical Analysis and Applications

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We study oscillatory properties of solutions of a functional differential equation of the formwhere n 2 and F : C(R + ; R) → L loc (R + ; R) is a continuous mapping. Sufficient conditions are established for this equation to have the so-called Property A. The obtained results are also new for the generalized Emden-Fowler type ordinary differential equation. The method by which the oscillatory properties of Eq. (0.1) are established enables one to obtain optimal conditions for (0.1) to have Property A for sufficiently general equations (for some classes of functions the obtained sufficient conditions are necessary as well).

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Linear functional differential equations with Property A

Cited by 7 publications

References 2 publications

Nonlinear functional differential equations with Properties A and B

Nonlinear functional differential equations with Properties A and B

Quasi-linear functional differential equations with Property A

On asymptotic behavior of solutions of n-TH order Emden-Fowler differential equations with advanced argument

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