Positive solutions of difference equations
Authors:
Ch. G. Philos and Y. G. Sficas
Journal:
Proc. Amer. Math. Soc. 108 (1990), 107115
MSC:
Primary 39A10
MathSciNet review:
1024260
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Abstract: Consider the difference equation where is a positive integer, is a sequence of positive real numbers and is a sequence of integers with . The characteristic equation of (E) is We prove the following theorem. Theorem. (i) For even, (E) has a positive solution with if and only if (*) has a root in . (ii) For odd, (E) has a positive solution if and only if (*) has a root in .
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 L. H. Erbe and B. G. Zhang, Oscillation of discrete analogues of delay equations, Differential and Integral Equations 2 (1989), 300309. MR 983682 (90a:39001)
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 I. Györi and G. Ladas, Linearized oscillations for equations with piecewise constant arguments, Differential and Integral Equations 2 (1989), 123131. MR 984181 (90a:34159)
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 G. Ladas, Oscillations of equations with piecewise constant mixed arguments, Proceedings of the International Conference on Theory and Applications of Differential Equations, March 2125, 1988, Ohio University. MR 1026200 (90m:34140)
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 G. Ladas, Ch. G. Philos and Y. G. Sficas, Necessary and sufficient conditions for the oscillation of difference equations Libertas Math. 9 (1989). MR 1048252 (91b:39003)
 [5]
 G. Ladas, Y. G. Sficas and I. P. Stavroulakis, Necessary and sufficient conditions for oscillations of higher order delay differential equations, Trans. Amer. Math. Soc. 285 (1984), 8190. MR 748831 (85j:34146)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939199010242605
PII:
S 00029939(1990)10242605
Keywords:
Difference equation,
solution,
positive solution
Article copyright:
© Copyright 1990
American Mathematical Society
