Oscillation of certain second-order nonlinear differential equations

In this paper we consider the second-order nonlinear differential equation [a(t)(y'(t))(sigma)]' + q(t)f(y(t)) = 0, (*) where sigma > 0 is any quotient of odd integers, a is an element of C-1(R,(0,infinity)), q is an element of C(R,R), f is an element of C(R,R), xf(x)>0, f'(x)greater than or equal to 0 for x not equal 0. Some new sufficient conditions for the oscillation of all solutions of (*) are obtained. Several examples that dwell upon the importance of our results are also included. (C) 1998 Academic Press.