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Kaizhong Guan, Jianhua Shen

Oscillation of first order neutral differential equations of Euler form

Keywords: oscillation, neutral differential equation, variable unbounded delay, Euler form

In this paper, we investigate the first order neutral differential equation of Euler form with variable unbounded delay

d/dt(x(t)-cx(αt))+1/t∑_i=1ⁿp_ix(β_i t)=0, t ≥ t₀ > 0, (*)

where 0 ≤ c < 1, 0 < α < 1, 0 < β_i < 1 and p_i > 0 are constants, i=1,2,…,n. Some necessary and sufficient as well as explicit sufficient conditions for the oscillation of all solutions are established.

Analysis, Oldenbourg Wissenschaftsverlag

Print ISSN: 0174-4747
Volume: 27, 01/2007
Pages: 061 - 072

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