Linear perturbations of a nonoscillatory second order equation
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- by William F. Trench
- Proc. Amer. Math. Soc. 97 (1986), 423-428
- DOI: https://doi.org/10.1090/S0002-9939-1986-0840623-1
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Abstract:
It is shown that the equation $(r(t)x’)’ + g(t)x = 0$ has solutions which behave asymptotically like those of a nonoscillatory equation $(r(t)y’)’ + f(t)y = 0$, provided that a certain integral involving $f - g$ converges (perhaps conditionally) and satisfies a second condition which has to do with its order of convergence. The result improves upon a theorem of Hartman and Wintner.References
- Philip Hartman, Ordinary differential equations, John Wiley & Sons, Inc., New York-London-Sydney, 1964. MR 0171038
- William F. Trench, Functional perturbations of second order differential equations, SIAM J. Math. Anal. 16 (1985), no. 4, 741–756. MR 793919, DOI 10.1137/0516056
Bibliographic Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 97 (1986), 423-428
- MSC: Primary 34C10
- DOI: https://doi.org/10.1090/S0002-9939-1986-0840623-1
- MathSciNet review: 840623