ON EXISTENCE OF POSITIVE SOLUTIONS OF NEUTRAL DIFFERENCE EQUATIONS
Keyword(s):
Consider the neutral difference equation \[\Delta(x_n- cx_{n-m})+p_nx_{n-k}=0, n\ge N\qquad (*) \] where $c$ and $p_n$ are real numbers, $k$ and $N$ are nonnegative integers, and $m$ is positive integer. We show that if \[\sum_{n=N}^\infty |p_n|<\infty \qquad (**) \] then Eq.(*) has a positive solution when $c \neq 1$. However, an interesting example is also given which shows that (**) does not imply that (*) has a positive solution when $c =1$.
2018 ◽
Vol 2018
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pp. 1-13
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2004 ◽
Vol 152
(2)
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pp. 351-366
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2014 ◽
Vol 2014
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pp. 1-4
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1991 ◽
Vol 158
(1)
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pp. 213-233
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