The existence of at least one unbounded positive solution and the existence of multiple unbounded positive solutions are established for the singular second-order boundary value problem p(t)-1(p(t)x′(t))′ + Φ(t)f(t,x,px′) = 0, 0 < t < +∞, x(0) = 0, limt→+∞p(t)x′(t) = 0, using the fixed point index, where f may be singular at px′ = 0.
