Positive solutions of singular boundary value problem of negative exponent Emden–Fowler equation

αu(0)−β u(0) = 0, γu(1)+ δu(1) = 0, (2) where α,β ,γ,δ ≥ 0,λ ∈ R and ρ := γβ + αγ + αδ > 0; p ∈ C((0,1), [0,∞)) and may be singular at t = 0,t = 1. When λ < 0, see [3,4,7,8] for the result concerning the above problem. When λ > 0, [6] shows the existence and uniqueness to (1) and (2) in the case of β = δ = 0 by means of the shooting method. For the following problem u + p(t)u−λ(t)+ q(t)u(t) = 0, 0 < t < 1, (3)