Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/7754
Title: Rectifiable oscillations in second-order linear differential equations
Authors: Kwong, MK
Pasic, M
Wong, JSW
Keywords: Co-existence
Fractal dimension
Graph
Integral criterion
Linear equation
Oscillation
Rectifiability
Stability
Issue Date: 2008
Publisher: Academic Press Inc Elsevier Science
Source: Journal of differential equations, 2008, v. 245, no. 8, p. 2333-2351 How to cite?
Journal: Journal of Differential Equations 
Abstract: We study the linear differential equation (P) : y″ (x) + f (x) y (x) = 0, on I = (0, 1), where the coefficient f (x) is strictly positive and continuous on I, and satisfies the Hartman-Wintner condition at x = 0. The four main results of the paper are: (i) a criterion for rectifiable oscillations of (P), characterized by the integrability of root(f (x), 4) on I; (ii) a stability result for rectifiable and unrectifiable oscillations of (P), in terms of a perturbation on f (x); (iii) the s-dimensional fractal oscillations (for which we assume also f (x) ∼ c x- α when x → 0, α > 2, and s = max {1, 3 / 2 - 2 / α}); and (iv) the co-existence of rectifiable and unrectifiable oscillations in the absence of the Hartman-Wintner condition on f (x). Explicit examples related to the above results are given.
URI: http://hdl.handle.net/10397/7754
DOI: 10.1016/j.jde.2008.05.016
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