Oscillation theorems for superlinear second-order damped differential equations

Abstract

In this paper, we concerned with the oscillation of the second-order superlinear differential equation of the form ( a ( t ) y ′ ( t ) ) ′ + p ( t ) y ′ ( t ) + q ( t ) f ( y ( t ) ) = 0 . Several new oscillation criteria are established under quite general assumptions. Our methodology is somewhat different from that of previous authors [Ch.G. Philos, Oscillation theorems for linear differential equations of second order, Arch. Math. (Basel) 53 (1989) 482–492; Ch.G. Philos, Oscillation criteria for second order superlinear differential equations, Canad. J. Math. Anal. XLI (1989) 321–340; CH.G. Philos, I.K. Purnaras, Oscillations in superlinear differential equations of second order. J. Math. Anal. Appl. 165 (1992) 1–11; Y.H. Yu, Oscillation criteria for second order nonlinear differential equations with damping, Acta. Math. Appl. 16 (1993) 433–441 (in Chinese)]. Our results generalize and extend some earlier results of Yu (1993). Example is also given to illustrate the results.