Positive solutions of difference equations

Authors:
Ch. G. Philos and Y. G. Sficas

Journal:
Proc. Amer. Math. Soc. **108** (1990), 107-115

MSC:
Primary 39A10

DOI:
https://doi.org/10.1090/S0002-9939-1990-1024260-5

MathSciNet review:
1024260

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Abstract | References | Similar Articles | Additional Information

Abstract: Consider the difference equation

**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* .

**[1]**L. H. Erbe and B. G. Zhang,*Oscillation of discrete analogues of delay equations*, Differential and Integral Equations**2**(1989), 300-309. MR**983682 (90a:39001)****[2]**I. Györi and G. Ladas,*Linearized oscillations for equations with piecewise constant arguments*, Differential and Integral Equations**2**(1989), 123-131. MR**984181 (90a:34159)****[3]**G. Ladas,*Oscillations of equations with piecewise constant mixed arguments*, Proceedings of the International Conference on Theory and Applications of Differential Equations, March 21-25, 1988, Ohio University. MR**1026200 (90m:34140)****[4]**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), 81-90. MR**748831 (85j:34146)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1990-1024260-5

Keywords:
Difference equation,
solution,
positive solution

Article copyright:
© Copyright 1990
American Mathematical Society