×

On the oscillation of nonlinear two-dimensional differential systems. (English) Zbl 0897.34033

Summary: An oscillation criterion is given for a certain form of nonlinear two-dimensional differential systems. This criterion originated in a well-known oscillation result due to W. J. Coles [Ann. Mat. Pura Appl., IV. Ser. 82, 123-133 (1969; Zbl 0188.15304)] (as extended and improved by J. S. W. Wong [SIAM J. Appl. Math. 14, 724-728 (1966; Zbl 0145.33702), Proc. Am. Math. Soc. 106, No. 4, 1069-1077 (1989; Zbl 0694.34027), ibid. 115, No. 2, 389-395 (1992; Zbl 0760.34032)] concerning second-order nonlinear differential equations with alternating coefficients.

MSC:

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

References:

[1] F. V. Atkinson, On second order nonlinear oscillation, Pacific J. Math. 5 (1955), 643-647. · Zbl 0065.32001
[2] Štefan Belohorec, Non-linear oscillations of a certain non-linear second-order differential equation, Mat.-Fyz. asopis Sloven. Akad. Vied 12 (1962), 253 – 262 (Slovak, with English summary). · Zbl 0129.06607
[3] W. J. Coles, Oscillation criteria for nonlinear second order equations, Ann. Mat. Pura Appl. (4) 82 (1969), 123 – 133. · Zbl 0188.15304 · doi:10.1007/BF02410793
[4] Man Kam Kwong and James S. W. Wong, An application of integral inequality to second order nonlinear oscillation, J. Differential Equations 46 (1982), no. 1, 63 – 77. · Zbl 0503.34021 · doi:10.1016/0022-0396(82)90110-3
[5] Man Kam Kwong and James S. W. Wong, Oscillation of Emden-Fowler systems, Differential Integral Equations 1 (1988), no. 2, 133 – 141. · Zbl 0715.34059
[6] D. D. Mirzov, The oscillatoriness of the solutions of a system of nonlinear differential equations, Differencial\(^{\prime}\)nye Uravnenija 9 (1973), 581 – 583, 592 (Russian).
[7] D. D. Mirzov, On the question of the oscillation of the solutions of a system of nonlinear differential equations, Mat. Zametki 16 (1974), 571 – 576 (Russian).
[8] D. D. Mirzov, The oscillatory nature of the solutions of a nonlinear differential system of Emden-Fowler type, Differentsial\(^{\prime}\)nye Uravneniya 16 (1980), no. 11, 1980 – 1984, 2108 (Russian).
[9] Paul Waltman, An oscillation criterion for a nonlinear second order equation, J. Math. Anal. Appl. 10 (1965), 439 – 441. · Zbl 0131.08902 · doi:10.1016/0022-247X(65)90138-1
[10] James S. W. Wong, On two theorems of Waltman, SIAM J. Appl. Math. 14 (1966), 724 – 728. · Zbl 0145.33702 · doi:10.1137/0114061
[11] James S. W. Wong, Oscillation theorems for second order nonlinear differential equations, Proc. Amer. Math. Soc. 106 (1989), no. 4, 1069 – 1077. · Zbl 0694.34027
[12] James S. W. Wong, Oscillation criteria for second order nonlinear differential equations with integrable coefficients, Proc. Amer. Math. Soc. 115 (1992), no. 2, 389 – 395. · Zbl 0760.34032
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.