The authors present several oscillation theorems for differential equation of second order （r（t）g（φ（x（t））x＇（t））＇＋q（t） f （x（t）） = 0and for differential equation with damping term Mx＂（t） ＋ p（t...The authors present several oscillation theorems for differential equation of second order （r（t）g（φ（x（t））x＇（t））＇＋q（t） f （x（t）） = 0and for differential equation with damping term Mx＂（t） ＋ p（t）x＇（t） ＋ q（t）x（t）=0where M〉 0, r（t） is positive continuous function. The conclusion is based also on building function where coefficients are involved in the equation and positive functions used by Philo H（t, s） and averaging techniques. Our results generalized, extend to some already known oscillation criteria in the literature. Also, here we give some applications of oscillation solution of. （1） and （2）, wherep（t） and q（t） are positive. The original purposes of differential equation are the mathematical formulation of the vibration frequency and the amplitude profile of a vibrating string with friction which the mass may have to encounter air resistance in its motion and in electric circuit containing an ac voltage source, an indicator, a capacitor, and a resistor in series is analyzed mathematically, the equation that results is a second order linear differential equation with oscillatory solution.展开更多
文摘The authors present several oscillation theorems for differential equation of second order （r（t）g（φ（x（t））x＇（t））＇＋q（t） f （x（t）） = 0and for differential equation with damping term Mx＂（t） ＋ p（t）x＇（t） ＋ q（t）x（t）=0where M〉 0, r（t） is positive continuous function. The conclusion is based also on building function where coefficients are involved in the equation and positive functions used by Philo H（t, s） and averaging techniques. Our results generalized, extend to some already known oscillation criteria in the literature. Also, here we give some applications of oscillation solution of. （1） and （2）, wherep（t） and q（t） are positive. The original purposes of differential equation are the mathematical formulation of the vibration frequency and the amplitude profile of a vibrating string with friction which the mass may have to encounter air resistance in its motion and in electric circuit containing an ac voltage source, an indicator, a capacitor, and a resistor in series is analyzed mathematically, the equation that results is a second order linear differential equation with oscillatory solution.
