Oscillation criteria for second order nonlinear differential equations involving general means

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.