Abstract
In this paper, we obtain the sufficient and necessary conditions for all solutions of the odd-order nonlinear delay differential equation.x (n)+Q(t)f(x(g(t)))=0 to be oscillatory. In particular, ifn=1, Q(t)>0, f(x)=x α, where α∈(0,1) and is a ratio of odd integers andg(t)=t−ϑ for some ϑ>0, then every solution of (*) oscillates if and only if ∫∞Q(s)ds=∞.
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Das, P. Oscillation of odd order delay differential equations. Proc. Indian Acad. Sci. (Math. Sci.) 103, 341–347 (1993). https://doi.org/10.1007/BF02866997
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DOI: https://doi.org/10.1007/BF02866997