×

Oscillation theorems for nonlinear differential equations of second order. (English) Zbl 0767.34017

Oscillation criteria are obtained for nonlinear differential equations of the type (1) \([rg(x)x']'+px'=qf(x)\), where \(p\), \(q\), \(r\) are real-valued continuous functions in a non-negative interval \([t_ 0,\infty)\), \(f\), \(g\) are real-valued continuous functions in \((-\infty,\infty)\), \(r(t)>0\) in \([t_ 0,\infty)\), \(xf(x)>0\), and \(g(x)>0\) for all \(x\neq 0\). The theorems generalize several earlier ones of similar type.

MSC:

34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Grace, S. R., Oscillation criteria for second order differential equations with damping, J. Austral. Math. Soc. Ser. A, 49, 43-54 (1990) · Zbl 0725.34030
[2] Grace, S. R., Oscillation theorems for second order nonlinear differential equations with damping, Math. Nachr., 14, 117-127 (1989) · Zbl 0673.34041
[3] Grace, S. R.; Lalli, B. S., Oscillatory behavior of solutions of second order differential equations with alternating coefficients, Math. Nachr., 127, 165-175 (1986) · Zbl 0615.34033
[4] Grace, S. R.; Lalli, B. S., Oscillation theorems for certain second order perturbed nonlinear differential equations, J. Math. Anal. Appl., 77, 205-214 (1980) · Zbl 0443.34031
[5] 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
[6] Grace, S. R.; Lalli, B. S.; Yeh, C. C., Oscillations theorems for nonlinear second order differential equations with a nonlinear damping term, SIAM J. Math. Anal., 15, 1082-1093 (1984) · Zbl 0563.34042
[7] Grace, S. R.; Lalli, B. S.; Yeh, C. C., Addendum: Oscillation theorems for nonlinear second order differential equations with a nonlinear damping term, SIAM. J. Math. Anal., 19, 1252-1253 (1988) · Zbl 0651.34028
[8] Kamenev, I. V., Integral criterion for oscillation of linear differential equations of second order, Mat. Zametki, 23, 249-251 (1978), [In Russian] · Zbl 0386.34032
[9] Ch. G. PhilosArch. Math.; Ch. G. PhilosArch. Math. · Zbl 0661.34030
[10] Philos, Ch. G., Oscillation criteria for second order superlinear differential equations, Canad. J. Math., 41, 321-340 (1989) · Zbl 0666.34038
[11] Wintner, A., A criterion of oscillatory stability, Quart. Appl. Math., 7, 115-117 (1949) · Zbl 0032.34801
[12] Wong, J. S.W., An oscillation criterion for second order nonlinear differential equations, (Proc. Amer. Math. Soc., 98 (1986)), 109-112 · Zbl 0603.34025
[13] Yan, J., Oscillation theorems for scond order linear differential equations with damping, (Proc. Amer. Math. Soc., 98 (1986)), 276-282 · Zbl 0622.34027
[14] Yeh, C. C., Oscillation theorems for nonlinear second order differential equations with damping term, (Proc. Amer. Math. Soc., 84 (1982)), 397-402 · Zbl 0498.34023
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.