×

On oscillation of nonlinear second-order differential equations with damping term. (English) Zbl 1061.34021

Authors’ abstract: The paper is concerned with oscillation of a novel class of nonlinear differential equations with a damping term. First, it is demonstrated how known oscillation results for another intensively studied class of equations can be translated to the one in question, and vice versa. Advantages and drawbacks of such translation are carefully examined. Then, an oscillation criterion for the new class of equations is established. The main result of the paper is compared with those reported in the literature, and an illustrative example to which known oscillation criteria fail to apply is provided.

MSC:

34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Ayanlar, B.; Tiryaki, A., Oscillation theorems for nonlinear second order differential equations with damping, Acta math. hungar, 89, 1-13, (2000) · Zbl 0973.34021
[2] Kirane, M.; Rogovchenko, Yu.V., Oscillation results for a second order damped differential equation with nonmonotonous nonlinearity, J. math. anal. appl, 250, 118-138, (2000) · Zbl 1008.34029
[3] Rogovchenko, S.P.; Rogovchenko, Yu.V., Oscillation of second order differential equations with damping, Dynam. contin. discrete impuls. systems ser. A, 10, 447-461, (2003) · Zbl 1048.34071
[4] Rogovchenko, S.P.; Rogovchenko, Yu.V., Oscillation theorems for differential equations with a nonlinear damping term, J. math. anal. appl, 279, 139-152, (2003) · Zbl 1027.34040
[5] Tiryaki, A.; Zafer, A., Oscillation criteria for second order nonlinear differential equations with damping, Turkish J. math, 24, 185-196, (2000) · Zbl 0977.34027
[6] Grace, S.R., Oscillation theorems for second order nonlinear differential equations with damping, Math. nachr, 141, 117-127, (1989) · Zbl 0673.34041
[7] Grace, S.R., Oscillation theorems for nonlinear differential equations of second order, J. math. anal. appl, 171, 220-241, (1992) · Zbl 0767.34017
[8] Grace, S.R.; Lalli, B.S., Oscillations in second order differential equations with alternating coefficients, Period. math. hungar, 19, 69-78, (1988) · Zbl 0607.34031
[9] Grace, S.R.; Lalli, B.S., Oscillation theorems for nonlinear second order differential equations with a damping term, Comment. math. univ. carolin, 30, 691-697, (1989) · Zbl 0692.34030
[10] Grace, S.R.; Lalli, B.S., Integral averaging techniques for the oscillation of second order nonlinear differential equations, J. math. anal. appl, 149, 277-311, (1990) · Zbl 0697.34040
[11] Grace, S.R.; Lalli, B.S.; Yeh, C.C., Oscillation theorems for nonlinear second order differential equations with a nonlinear damping term, SIAM J. math. anal, 15, 1082-1093, (1984) · Zbl 0563.34042
[12] Kirane, M.; Rogovchenko, Yu.V., On oscillation of nonlinear second order differential equation with damping term, Appl. math. comput, 117, 177-192, (2001) · Zbl 1035.34019
[13] Grace, S.R., Oscillation criteria for second order nonlinear differential equations with damping, J. austral. math. soc. ser. A, 49, 43-54, (1990) · Zbl 0725.34030
[14] Grace, S.R.; Lalli, B.S., Oscillations of second order general nonlinear differential equations, (), 413-429 · Zbl 0832.34024
[15] Grace, S.R.; Lalli, B.S., Oscillation theorems for second order superlinear differential equations with damping, J. austral. math. soc. ser. A, 53, 156-165, (1992) · Zbl 0762.34012
[16] Grammatikopoulos, M.K., Oscillation theorems for second order ordinary differential inequalities and equations with alternating coefficients, An. stiint. univ. al. I. cuza, 26, 67-76, (1980) · Zbl 0442.34031
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.