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
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