Oscillation criteria for second order nonlinear differential equations with integrable coefficients

Author:
James S. W. Wong

Journal:
Proc. Amer. Math. Soc. **115** (1992), 389-395

MSC:
Primary 34C10

DOI:
https://doi.org/10.1090/S0002-9939-1992-1086346-0

MathSciNet review:
1086346

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Abstract: Consider the second order nonlinear differential equation where , and for . Furthermore, also satisfies either a superlinear or a sublinear condition, which covers the prototype nonlinear function with and respectively. The coefficient is allowed to be negative for arbitrarily large values of and is integrable in the sense that the improper interval exists for each . Oscillation criteria involving integrals of due to Coles and Butler for the superlinear and sublinear cases are shown to remain valid without the additional hypothesis that .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1992-1086346-0

Keywords:
Second order,
nonlinear,
ordinary differential equations,
oscillation,
asymptotic behavior

Article copyright:
© Copyright 1992
American Mathematical Society