OSCILLATION CRITERIA FOR HIGHER ORDER SUBLINEAR DELAY DIFFERENTIAL EQUATIONS
Journal Title: Дослідження в математиці і механіці - Year 2018, Vol 23, Issue 1
Abstract
In the interval [a,+∞[, the sublinear differential equations of order n⩾2 are considered. A solution of such equation is called proper if it is not identically equal to zero in any neighbourhood of +∞. The proper solution is called oscillatory if it changes its sign in any neighbourhood of +∞. We say that the equation has property A if every its proper solution for n even is oscillatory, and for n odd either oscillatory or monotone and vanishing at infinity together with their derivatives up to order n−1, inclusive. To investigate oscillatory properties of the above-mentioned equations the sets \linebreak Msub([a,+∞[×R) and M˜sub([a,+∞[×R) of sublinear with respect to the second argument continuous functions f:[a,+∞[×R→R are introduced (see Definitions \ref def:1
Authors and Affiliations
I. Kiguradze, T. Kiguradze
Keywords
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- DOI 10.18524/2519-206x.2018.1(31).134625
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