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

We study the second order Emden-Fowler equation y"(t) + a (x)\y\(gamma) sgn = 0, gamma > 0, where a(x) is a positive and absolutely continuous function on (0, infinity). Let phi(x) = a(x)x((gamma+3)/2), y not equal 1, and bounded away from zero. We prove the following theorem. If phi'_(x) is an element of L-1 (0, infinity) where phi'_(x) = - min(phi'(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. (C) 2003 Elsevier Science (USA). All rights reserved.