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

Abstract

We study the second order Emden–Fowler equation

(E)$$\text{y″(t)+a(x)|y|}{}^{\mathrm{\gamma }}\text{sgn}\text{y=0,}\text{γ>0,}$$

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.