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We consider the singular boundary value problem −r(x)y ′ (x) + q(x)y(x) = f (x), x ∈ R lim |x|→∞ y(x) = 0, where f ∈ L p (R), p ∈ [1, ∞] (L ∞ (R) := C(R)), r is a continuous positive function for x ∈ R, q ∈ L loc 1 (R), q ≥ 0. A solution of this problem is, by definition, any absolutely continuous function y satisfying the limit condition and almost… (More)
We consider an equation y ′′ (x) = q(x)y(x), x ∈ R (1) under the following assumptions on q(x) : 0 ≤ q(x) ∈ L loc 1 (R), x −∞ q(t)dt > 0, ∞ x q(t)dt > 0 for all x ∈ R. (2) Let v(x) (resp. u(x)) be a positive non-decreasing (resp. non-increasing) solution of (1) such that v ′ (x)u(x) − u ′ (x)v(x) = 1, x ∈ R. These properties determine u(x) and v(x) up to… (More)
Changes in the "momentary" pulse characteristics serve as a possible background to establishing a tentative diagnosis of arrhythmias. The method is based on the evaluation of alternation of shortened and lengthened intervals between cardiac contractions and also on the appearance of isolated shortened or lengthened intervals between cardiac contractions.