Asymptotic behavior of non-oscillatory solutions of first-order neutral difference equations (Q2850050)
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scientific article; zbMATH DE number 6212305
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Asymptotic behavior of non-oscillatory solutions of first-order neutral difference equations |
scientific article; zbMATH DE number 6212305 |
Statements
26 September 2013
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retarded argument
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deviated argument
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oscillatory solutions
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nonoscillatory solutions
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difference equations
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bounded solutions
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unbounded solutions
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asymptotic behavior
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Asymptotic behavior of non-oscillatory solutions of first-order neutral difference equations (English)
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Considering a first-order neutral difference equation of the form NEWLINE\[NEWLINE \Delta [ x(n) + c x(\tau(n))] + p(n) x(\sigma(n))=0, NEWLINE\]NEWLINE studying the asymptotic behavior of nonoscillatory solutions of the equation under the condition \( \sum _{i=0}^{\infty} p(i) = +\infty \) is not always necessary. By assuming various cases on the sign of the coefficients \( p(n)\), the asymptotic behavior of nonoscillatory solutions of the equation is analyzed providing interesting examples along with historical developments of the problem and a rich list of literature.
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