Sharp conditions for the oscillation of delay difference equations
1989 ◽
Vol 2
(2)
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pp. 101-111
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Keyword(s):
Suppose that {pn} is a nonnegative sequence of real numbers and let k be a positive integer. We prove that limn→∞inf [1k∑i=n−kn−1pi]>kk(k+1)k+1 is a sufficient condition for the oscillation of all solutions of the delay difference equation An+1−An+pnAn−k=0, n=0,1,2,…. This result is sharp in that the lower bound kk/(k+1)k+1 in the condition cannot be improved. Some results on difference inequalities and the existence of positive solutions are also presented.
2018 ◽
Vol 2018
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pp. 1-13
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2001 ◽
Vol 32
(4)
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pp. 275-280
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2011 ◽
Vol 50-51
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pp. 761-765
2007 ◽
Vol 2007
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pp. 1-16
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Keyword(s):
2001 ◽
Vol 28
(5)
◽
pp. 301-306
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