A nonoscillation theorem for Emden–Fowler equations

AbstractWe 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.TheoremLet γ≠1. If ψ(x) satisfies (a)limx→∞ψ(x)=k>0 and(b)∫∞|ψ′(x)|dx<∞, then Eq. (E) is nonoscillatory