Sign-changing first derivative of positive solutions of forced second-order nonlinear differential equations

Some oscillatory phenomena in physics, population, biomedicine and biochemistry are described by positive functions having sign-changing first derivative. Here, it is studied for all positive not necessarily periodic solutions of a large class of second-order nonlinear differential equations. It is based on a new reciprocal principle by which the classic oscillations of corresponding reciprocal linear equation causes the sign-changing first derivative of every positive solution of the main equation.