Naslov
Rectifiable oscillations in second-order linear differential equations

Autori
Kwong, Man Kam ; Pašić, Mervan ; Wong, James S.W.

Izvornik
Journal of Differential Equations (0022-0396) 245 (2008), 8; 2333-2351

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
linear equation; oscillation; graph; rectifiability; integral criterion; stability; co-existence; fractal dimension

Sažetak
We study the linear differential equation , 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 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)cx− 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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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