On existence of oscillatory solutions of second order Emden–Fowler equations

AbstractWe study the second order Emden–Fowler equation (E)y″(t)+a(x)|y|γsgny=0,γ>0, where a(x) is a positive and absolutely continuous function on (0,∞). Let φ(x)=a(x)x(γ+3)/2, γ≠1, and bounded away from zero. We prove the following theorem. If φ−′(x)∈L1(0,∞) where φ−′(x)=−min(φ′(x),0), then Eq. (E) has oscillatory solutions. In particular, this result embodies earlier results by Jasny, Kurzweil, Heidel and Hinton, Chiou, and Erbe and Muldowney