Abstract: New existence results are presented for the singular second-order nonlinear boundary value problems u″+g(t)f(u)=0, 0<t<1, αu(0)-βu′(0)=0, γu(1)+ δu′(1)=0 under the conditions 0≤f₀⁺<M₁, m₁<f_∞^-≤∞ or 0≤f_∞⁺<M₁, m₁<f₀^-≤∞, where f₀⁺= lim_u→0 f(u)/u, f_∞^-= lim_u→∞ f(u)/u, f₀^-= lim_u→0 f(u)/u, f_∞⁺= lim_u→∞ f(u)/u, g may be singular at t=0 and/or t=1 The proof uses a fixed point theorem in cone theory.

Key words: second-order singular boundary value problems, positive solutions, cone, fixed point