A nonoscillation theorem for Emden–Fowler equations

We study the second order Emden–Fowler equation (E) y + a(x)|y|γ−1y = 0, γ>0 where a(x) is positive and absolutely continuous on (0,∞). Let ψ(x) = x(γ+3)/2+δ where δ is any positive number. Theorem. Let γ = 1. If ψ(x) satisfies (a) limx→∞ψ(x) =k >0 and (b) ∞|ψ (x)|dx <∞, then Eq. (E) is nonoscillatory.  2002 Elsevier Science (USA). All rights reserved