An oscillation theorem for second order sublinear differential equations
HTML articles powered by AMS MathViewer
- by James S. W. Wong PDF
- Proc. Amer. Math. Soc. 110 (1990), 633-637 Request permission
Abstract:
An oscillation criterion is given for the second order sublinear differential equation $x'' + a(t){\left | x \right |^\gamma }\operatorname {sgn} x = 0,0 < \gamma < 1$, where the coefficient $a(t)$ is not assumed to be nonnegative for all large values of $t$. The result extends a condition recently discovered by Butler, Erbe, and Mingarelli for the linear equation.References
- G. J. Butler, Integral averages and the oscillation of second order ordinary differential equations, SIAM J. Math. Anal. 11 (1980), no. 1, 190–200. MR 556509, DOI 10.1137/0511017
- G. J. Butler, L. H. Erbe, and A. B. Mingarelli, Riccati techniques and variational principles in oscillation theory for linear systems, Trans. Amer. Math. Soc. 303 (1987), no. 1, 263–282. MR 896022, DOI 10.1090/S0002-9947-1987-0896022-5
- Philip Hartman, On non-oscillatory linear differential equations of second order, Amer. J. Math. 74 (1952), 389–400. MR 48667, DOI 10.2307/2372004 —, Ordinary differential equations, 2nd. ed., Wiley, New York, 1973.
- Philip Hartman, On nonoscillatory linear differential equations of second order, Proc. Amer. Math. Soc. 64 (1977), no. 2, 251–259. MR 463565, DOI 10.1090/S0002-9939-1977-0463565-7
- I. V. Kamenev, Certain specifically nonlinear oscillation theorems, Mat. Zametki 10 (1971), 129–134 (Russian). MR 287077
- I. V. Kamenev, An integral test for conjugacy for second order linear differential equations, Mat. Zametki 23 (1978), no. 2, 249–251 (Russian). MR 486798
- Man Kam Kwong and James S. W. Wong, Linearization of second-order nonlinear oscillation theorems, Trans. Amer. Math. Soc. 279 (1983), no. 2, 705–722. MR 709578, DOI 10.1090/S0002-9947-1983-0709578-6
- D. Willett, Classification of second order linear differential equations with respect to oscillation, Advances in Math. 3 (1969), 594–623. MR 280800, DOI 10.1016/0001-8708(69)90011-5
- Aurel Wintner, A criterion of oscillatory stability, Quart. Appl. Math. 7 (1949), 115–117. MR 28499, DOI 10.1090/S0033-569X-1949-28499-6
- James S. W. Wong, Oscillation theorems for second order nonlinear differential equations, Bull. Inst. Math. Acad. Sinica 3 (1975), no. 2, 283–309. MR 390372
- James S. W. Wong, An oscillation criterion for second order nonlinear differential equations, Proc. Amer. Math. Soc. 98 (1986), no. 1, 109–112. MR 848886, DOI 10.1090/S0002-9939-1986-0848886-3
- James S. W. Wong, An oscillation criterion for second order sublinear differential equations, Oscillations, bifurcation and chaos (Toronto, Ont., 1986) CMS Conf. Proc., vol. 8, Amer. Math. Soc., Providence, RI, 1987, pp. 299–302. MR 909919
- James S. W. Wong, Oscillation theorems for second order nonlinear differential equations, Proc. Amer. Math. Soc. 106 (1989), no. 4, 1069–1077. MR 952324, DOI 10.1090/S0002-9939-1989-0952324-2
Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 110 (1990), 633-637
- MSC: Primary 34C10
- DOI: https://doi.org/10.1090/S0002-9939-1990-1000170-4
- MathSciNet review: 1000170