Abstract
We study the second order Emden–Fowler equation (E) y″(t)+a(x)|y| γ sgny=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)∈ L 1(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.
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