Oscillatory and Asymptotic Properties of First Order Delay Neutral Differential Equations with Nonpositive Coefficients
Received:February 01, 1989  Revised:July 05, 1991
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He Xuezhong Ningxia University 
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Abstract:
      In this paper, we deal with the osicllatory and asymptotic properties of the solutions for the neutral delay differential equations d/(dt)[x(t)+p(t)x(t-τ)]-Q(t)x(t-σ(t))=0,t≥t0 and d/(dt)[x(t)+p(t)x(t-τ(t))]-Q(t)f(x(t-σ(t)))=0,t≥t0,where p(t)∈C([t0,+∞,R),Q(t)∈C([t0,+∞),R+),τ(t),σ(t)∈C([t0,+∞),R+), f∈C(R,R),f(u)u>0(u≠0). Some sufficient Conditions which keep all the boundedsolutions oscillating and all the solutions tending to zero or±∞(as t→+∞) are obtained.
Citation:
DOI:10.3770/j.issn:1000-341X.1991.04.028
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