Trench, William F. Linear perturbations of a nonoscillatory second order equation. (English) Zbl 0594.34057 Proc. Am. Math. Soc. 97, 423-428 (1986). Summary: 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. Cited in 1 ReviewCited in 12 Documents MSC: 34E10 Perturbations, asymptotics of solutions to ordinary differential equations 34D10 Perturbations of ordinary differential equations 34C99 Qualitative theory for ordinary differential equations Keywords:second order differential equation; nonoscillatory equation PDFBibTeX XMLCite \textit{W. F. Trench}, Proc. Am. Math. Soc. 97, 423--428 (1986; Zbl 0594.34057) Full Text: DOI References: [1] Philip Hartman, Ordinary differential equations, John Wiley & Sons, Inc., New York-London-Sydney, 1964. · Zbl 0123.21502 [2] William F. Trench, Functional perturbations of second order differential equations, SIAM J. Math. Anal. 16 (1985), no. 4, 741 – 756. · Zbl 0577.34060 · doi:10.1137/0516056 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.