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

MathSciNet review:
1024260

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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 Integral Equations**2**(1989), no. 3, 300–309. MR**983682****[2]**I. Győri and G. Ladas,*Linearized oscillations for equations with piecewise constant arguments*, Differential Integral Equations**2**(1989), no. 2, 123–131. MR**984181****[3]**G. Ladas,*Oscillations of equations with piecewise constant mixed arguments*, Differential equations and applications, Vol. I, II (Columbus, OH, 1988), Ohio Univ. Press, Athens, OH, 1989, pp. 64–69. MR**1026200****[4]**G. Ladas, Ch. G. Philos, and Y. G. Sficas,*Necessary and sufficient conditions for the oscillation of difference equations*, Libertas Math.**9**(1989), 121–125. MR**1048252****[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), no. 1, 81–90. MR**748831**, 10.1090/S0002-9947-1984-0748831-8

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

Keywords:
Difference equation,
solution,
positive solution

Article copyright:
© Copyright 1990
American Mathematical Society