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In this paper, the authors study the existence of positive solution of the followingBVP{1/p(t)(p(t)x′)′+ f(t,x(t),p(t)x′(t)) = 0,0＜t＜+∞αx(0) - β limt→0(t)x′(t) = 0, γ limt→∞ x(t) + δt→+∞lim p(t)x′(t) = 0on the semi-infinite interval. By considering characterization of the nonlinearity, they obtain some new existence results.