Abstract: In this paper, we discuss higher order sublinear functional differential equation
x⁽ⁿ⁾(t)+p(t)x^v(g(t))=0 t ≥ t⁰
where n ≥ 2,0 < v < 1,p(t)∈C(R₊,R₊),g(t)∈C([t₀,∞),R₊),0 ≤ g(t) ≤ t (t ≥ t₀) and
lim_t→∞g(t)=∞.R₊=[0,∞).
Some necessary and sufficient conditions for existence of positive solution of the equation are established.