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MATHEMATICA BOHEMICA, Vol. 131, No. 4, pp. 347-363 (2006)
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#
Asymptotic properties for half-linear

difference equations

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Mariella Cecchi, Zuzana Dosla, Mauro Marini, Ivo Vrkoc

* Mariella Cecchi*, Depart. of Electronics and Telecomunications, University of Florence, Via S. Marta 3, 50139 Firenze, Italy, e-mail: ` mariella.cecchi@unifi.it`; * Zuzana Dosla*, Depart. of Mathematics, Masaryk University, Janackovo nam. 2a, 602 00 Brno, Czech Republic, e-mail: ` dosla@math.muni.cz`; * Mauro Marini*, Depart. of Electronics and Telecomunications, University of Florence, Via S. Marta 3, 50139 Firenze, Italy, e-mail: ` mauro.marini@unifi.it`; * Ivo Vrkoc*, Mathematical Institute of the Academy of Sciences, Zitna 25, 115 67 Praha, Czech Republic, e-mail: ` vrkoc@math.cas.cz`

**Abstract:** Asymptotic properties of the half-linear difference equation

\Delta (a_{n}|\Delta x_{n}|^{\alpha }\sgn \Delta x_{n} )=b_{n}|x_{n+1}|^{\alpha }\sgn x_{n+1}\tag {$*$}

are investigated by means of some summation criteria. Recessive solutions and the Riccati difference equation associated to $(*)$ are considered too. Our approach is based on a classification of solutions of $(*)$ and on some summation inequalities for double series, which can be used also in other different contexts.

**Keywords:** half-linear second order difference equation, nonoscillatory solutions, Riccati difference equation, summation inequalities

**Classification (MSC2000):** 39A10

**Full text of the article:**

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