Eigenvalue characterization of a system of difference equations
We consider the following system of difference equations: ui(k) = λ∑gi(k, l)Pi(l, u1(l), u2(l), . . . , un(l)), k ∈ {0, 1, . . . }, 1 ≤ i ≤ n, where λ > 0 and T ≥ N ≥ 0. Our aim is to determine those values of λ such that the above system has a constant-sign solution. In addition, explicit...
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| Date: | 2004 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2004
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| Series: | Нелінійні коливання |
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/176990 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Eigenvalue characterization of a system of difference equations / R.P. Agarwal, D. O'Regan, P. J. Y. Wong // Нелінійні коливання. — 2004. — Т. 7, № 1. — С. 3-47. — Бібліогр.: 23 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | We consider the following system of difference equations:
ui(k) = λ∑gi(k, l)Pi(l, u1(l), u2(l), . . . , un(l)), k ∈ {0, 1, . . . }, 1 ≤ i ≤ n,
where λ > 0 and T ≥ N ≥ 0. Our aim is to determine those values of λ such that the above system
has a constant-sign solution. In addition, explicit intervals for λ will be presented. The generality of the
results obtained is illustrated through applications to several well known boundary-value problems. We
also extend the above problem to that on {0, 1, . . . },
ui(k) = λ∑gi(k, l)Pi(l, u1(l), u2(l), . . . , un(l)), k ∈ {0, 1, . . . , T}, 1 ≤ i ≤ n,
Finally, both systems above are extended to the general case when λ is replaced by λi
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