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Generalizations of an inequality of Kiguradze. (English) Zbl 0546.34010

For the differential equation \(d^ ny/dx^ n+yF(x,y)=0\), (with appropriate conditions on F), Kiguradze has shown that if \(y^{(i)}\geq 0\), \(i=0,1,...,k\), \(y^{(k+1)}\leq 0\) on (a,\(\infty)\), then (1) \((x- a)y^{(t+1)}\leq (k-t)y^{(t)} t=0,1,...,k\) on (a,\(\infty)\). In this note the author generalizes inequality (1) in various directions.
Reviewer: P.N.Bajaj

MSC:

34A40 Differential inequalities involving functions of a single real variable
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