On oscillations for solutions of $n$th order differential equations
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- by H. Onose PDF
- Proc. Amer. Math. Soc. 33 (1972), 495-500 Request permission
Abstract:
Necessary and sufficient conditions are given that all solutions of ${x^{(n)}} + f(t,x,xβ, \cdots ,{x^{(n - 2)}}) = 0$ are oscillatory for n even and are oscillatory or tend monotonically to zero as $t \to \infty$ for n odd. The results generalize recent results of J. S. W. Wong and G. H. Ryder and D. V. V. Wend.References
- Hiroshi Onose, Oscillatory properties of solutions of even order differential equations, Pacific J. Math. 38 (1971), 747β757. MR 306615, DOI 10.2140/pjm.1971.38.747
- Hiroshi Onose, Oscillatory property of ordinary differential equations of arbitrary order, J. Differential Equations 7 (1970), 454β458. MR 257465, DOI 10.1016/0022-0396(70)90093-8
- Gerald H. Ryder and David V. V. Wend, Oscillation of solutions of certain ordinary differential equations of $n\textrm {th}$ order, Proc. Amer. Math. Soc. 25 (1970), 463β469. MR 261091, DOI 10.1090/S0002-9939-1970-0261091-5
- James S. W. Wong, On second order nonlinear oscillation, Funkcial. Ekvac. 11 (1968), 207β234 (1969). MR 245915
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 33 (1972), 495-500
- MSC: Primary 34C10
- DOI: https://doi.org/10.1090/S0002-9939-1972-0296419-5
- MathSciNet review: 0296419