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

We study the second order Emden–Fowler equation y (t )+ a(x)|y|γ sgn y = 0, γ>0, (E) 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.  2003 Elsevier Science (USA). All rights reserved.