Oscillation criteria for second order nonlinear differential equations with damped term

Several oscillation criteria are given for the second order nonlinear differential equation with damping [a(t)y' (t)]' + p(t)x'(t) + q(t)f(y(t)) = 0, where a is an element of C-1 (R, (theta, infinity)), p(t) and q(t) are allowed to change sign on [t(0), infinity), and f is an element of C-1 (R, R) such that xf(x) > 0 for x not equal 0 and f'(x) greater than or equal to mu > 0. Our results do not need the usual hypothesis integral(infinity) 1/a(s)ds = infinity and extend some known oscillation criteria by using a generalized Riccati transformation u(t) = a(t)r(t) [y'(t)/f(y(t)) + g(t)], where g is an element of C-1 is a given function on [t(0), infinity) and r(s) is approximately equal to exp (-2 mu integral(s) (g(v) - p(v)/2 mu a(v))dv). Examples are inserted to illustrate our results.