Sufficient conditions for nonoscillation of a second order nonlinear differential equation

Graef, John R.; Spikes, Paul W.

doi:10.1090/S0002-9939-1975-0369808-0

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Sufficient conditions for nonoscillation of a second order nonlinear differential equation
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by John R. Graef and Paul W. Spikes PDF

Proc. Amer. Math. Soc. 50 (1975), 289-292 Request permission

Abstract:

Using a generalization of a variational theorem due to Leighton, the authors obtain sufficient conditions for the second order nonlinear differential equation $(a(t)x’)’ + q(t)f(x) = r(t)$ to be nonoscillatory. Examples showing the necessity of certain hypotheses are also given.

References

Vadim Komkov, A generalization of Leighton’s variational theorem, Applicable Anal. 2 (1972/73), 377–383. MR 414994, DOI 10.1080/00036817208839051
Walter Leighton, Comparison theorems for linear differential equations of second order, Proc. Amer. Math. Soc. 13 (1962), 603–610. MR 140759, DOI 10.1090/S0002-9939-1962-0140759-0