This paper is concerned with the mixed boundary value problem of the second order singular ordinary differential equation
[Φ(ρ(t)x'(t))]' + f(t, x(t), x'(t)) = 0, t ∈ R,
limt→−∞x(t) = ∫−∞+∞g(s, x(s), x'(s)) ds,
limt→+∞ρ(t)x'(t) = ∫−∞+∞h(s, x(s), x' (s)) ds.
Sufficient conditions to guarantee the existence of at least one positive solution are established. The emphasis is put on the one-dimensional p-Laplacian term [Φ(ρ(t)x'(t))]' involved with the nonnegative function ρ satisfying ∫−∞+∞1/ρ(s) ds = +∞.
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