Journal
ABSTRACT AND APPLIED ANALYSIS
Volume -, Issue -, Pages -Publisher
HINDAWI LTD
DOI: 10.1155/2014/168425
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- Sh. Rustaveli National Science Foundation [31/09]
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The following differential equation u((n))(t) + p(t)vertical bar u(sigma(t))vertical bar(mu(t)) sign u(sigma(t)) = 0 is considered. Here p epsilon L-loc (R+; R+), mu epsilon C(R+; (0,+ infinity)), sigma epsilon C(R+; R+), sigma(t) < t, and lim(t ->infinity)sigma(t) = +infinity. We say that the equation is almost linear if the condition lim(t ->infinity)mu(t) = 1 is fulfilled, while if lim sup(t ->infinity)mu(t) not equal 1 or lim inf(t ->infinity) mu(t) not equal 1, then the equation is an essentially nonlinear differential equation. In the case of almost linear and essentially nonlinear differential equations with advanced argument, oscillatory properties have been extensively studied, but there are no results on delay equations of this sort. In this paper, new sufficient conditions implying Property A for delay Emden-Fowler equations are obtained.
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