Oscillation criteria for second-order nonlinear differential equations with damping

Yuri V. Rogovchenko1,2, Fatoş Tuncay1
1Department of Mathematics, Eastern Mediterranean University, Famagusta, TRNC, Mersin 10, Turkey
2School of Pure and Applied Natural Sciences, University of Kalmar, SE-391 82 Kalmar, Sweden

Tài liệu tham khảo

Sturm, 1836, Sur les équations différentielles linéaires du second ordré, J. Math. Pures Appl., 1, 106 Agarwal, 2000 Agarwal, 2002 Erbe, 1995 Győri, 1991 Kreith, 1973 Ladde, 1987 Swanson, 1968 Bellman, 1953 Coppel, 1965 Kiguradze, 1993 Wong, 1968, A second order nonlinear oscillation, Funkcial. Ekvac., 11, 207 Wong, 1975, On the generalized Emden–Fowler equation, SIAM Rev., 17, 339, 10.1137/1017036 Wong, 2003, On an oscillation theorem of Waltman, Can. Appl. Math. Q, 11, 415 Baker, 1973, Oscillation theorems for a second order damped nonlinear differential equation, SIAM J. Math. Anal., 25, 37, 10.1137/0125007 Bobisud, 1970, Oscillation of solutions of damped nonlinear differential equations, SIAM J. Math. Anal., 18, 601, 10.1137/0119059 Butler, 1977, The oscillatory behavior of a second order nonlinear differential equation with damping, J. Math. Anal. Appl., 57, 273, 10.1016/0022-247X(77)90260-8 Elabbasy, 2005, Oscillation of second-order nonlinear differential equations with a damping term, Electron. J. Differential Equations, 13 Grace, 1989, Oscillation theorems for second order nonlinear differential equations with damping, Math. Nachr., 141, 117, 10.1002/mana.19891410114 Grace, 1990, Oscillation criteria for second order nonlinear differential equations with damping, J. Austral. Math. Soc. Ser. A, 49, 43, 10.1017/S1446788700030226 Grace, 1992, Oscillation theorems for nonlinear differential equations of second order, J. Math. Anal. Appl., 171, 220, 10.1016/0022-247X(92)90386-R Grace, 1988, Oscillations in second order differential equations with alternating coefficients, Period. Math. Hungar., 19, 69, 10.1007/BF01848010 Grace, 1989, Oscillation theorems for nonlinear second order differential equations with a damping term, Comment. Math. Univ. Carolin., 30, 691 Grace, 1990, Integral averaging technique for the oscillation of second order nonlinear differential equations, J. Math. Anal. Appl., 149, 277, 10.1016/0022-247X(90)90301-U Grace, 1992, Oscillation theorems for second order superlinear differential equations with damping, J. Austral. Math. Soc. Ser. A, 53, 156, 10.1017/S144678870003576X Grace, 1984, Oscillation theorems for nonlinear second order differential equations with a nonlinear damping term, SIAM J. Math. Anal., 15, 1082, 10.1137/0515084 Grace, 1988, Addendum: Oscillation theorems for nonlinear second order differential equations with a nonlinear damping term, SIAM J. Math. Anal., 19, 1252, 10.1137/0519089 Kamenev, 1978, An integral criterion for oscillation of linear differential equations, Mat. Zametki, 23, 249 Kirane, 2000, Oscillation results for a second order damped differential equation with nonmonotonous nonlinearity, J. Math. Anal. Appl., 250, 118, 10.1006/jmaa.2000.6975 Kirane, 2001, On oscillation of nonlinear second order differential equation with damping term, Appl. Math. Comput., 117, 177, 10.1016/S0096-3003(99)00172-1 Li, 2003, Interval oscillation criteria for second order nonlinear differential equations with damping, Taiwanese J. Math., 7, 461, 10.11650/twjm/1500558398 Li, 2000, Interval oscillation criteria for second order nonlinear differential equations with damping, Comput. Math. Appl., 40, 217, 10.1016/S0898-1221(00)00155-3 Li, 1999, Oscillation criteria for second order nonlinear differential equations with damped term, Indian J. Pure Appl. Math., 30, 1017 Manojlović, 2004, Oscillation criteria for sublinear differential equations with damping, Acta Math. Hungar., 104, 153, 10.1023/B:AMHU.0000034369.84782.0a Mustafa, 2004, On oscillation of nonlinear second-order differential equations with damping term, J. Math. Anal. Appl., 298, 604, 10.1016/j.jmaa.2004.05.029 Philos, 1989, Oscillation theorems for linear differential equations of second order, Arch. Math., 53, 483, 10.1007/BF01324723 Rogovchenko, 2003, Oscillation of differential equations with damping, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 10, 447 Rogovchenko, 2003, Oscillation results for general second-order differential equations with damping term, J. Math. Anal. Appl., 279, 139, 10.1016/S0022-247X(02)00623-6 Rogovchenko, 1997, Oscillation criteria for second order nonlinear perturbed differential equations, J. Math. Anal. Appl., 215, 334, 10.1006/jmaa.1997.5595 Rogovchenko, 2000, Oscillation theorems for second-order equations with damping, Nonlinear Anal., 41, 1005, 10.1016/S0362-546X(98)00324-1 Sun, 2004, New Kamenev-type oscillation criteria for second-order nonlinear differential equations with damping, J. Math. Anal. Appl., 291, 341, 10.1016/j.jmaa.2003.11.008 Tiryaki, 2000, Oscillation criteria for second order nonlinear differential equation with damping, Turkish J. Math., 24, 185 Tiryaki, 2005, Interval oscillation of a general class of second-order nonlinear differential equations with nonlinear damping, Nonlinear Anal., 60, 49, 10.1016/S0362-546X(04)00333-5 Wong, 2001, On Kamenev-type oscillation theorems for second-order differential equations with damping, J. Math. Anal. Appl., 258, 244, 10.1006/jmaa.2000.7376 Yan, 1986, Oscillation theorems for second order linear differential equations with damping, Proc. Amer. Math. Soc., 98, 276, 10.1090/S0002-9939-1986-0854033-4 Yang, 2003, Oscillation criteria for nonlinear differential equations with damping, Appl. Math. Comput., 136, 549, 10.1016/S0096-3003(02)00079-6 Yeh, 1982, Oscillation theorems for nonlinear second order differential equations with damping term, Proc. Amer. Math. Soc., 84, 397, 10.1090/S0002-9939-1982-0640240-9 Zheng, 2002, Note on Wong’s paper, J. Math. Anal. Appl., 274, 466, 10.1016/S0022-247X(02)00297-4