Consider the second order nonlinear differential equation (E) y " + a(t)f(y
) = 0 where a(t) is an element of C[0, infinity), f(y) is an element of C-1
(-infinity, infinity), f'(y) greater than or equal to 0, and yf(y) > 0 for
y not equal 0. Furthermore, f(y) also satisfies either a superlinear or a s
ublinear condition, which covers the nonlinear function f(y) = y\y\gamma(-1
) with gamma > 1 and 0 < gamma < 1, respectively, commonly known as the Emd
en-Fowler case. Here the coefficient function a(t) is allowed to be negativ
e for arbitrarily large values of t. Kamenev type oscillation criteria invo
lving integral averages for the linear equations (L) y " + a(t)y = 0 are ex
tended to the nonlinear equation (E) by using more general means. The resul
ts extend similar results on general means by Philos for the linear equatio
n (L) and also results based upon Kamenev's integral averaging method conce
rning the nonlinear equation (E). (C) 2000 Academic Press.