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 (MSC 2000): 39A10
Full text available as PDF (smallest), as compressed PostScript (.ps.gz) or as raw PostScript (.ps).
Access to the full text of journal articles on this site is restricted to the subscribers of Myris Trade. To activate your access, please contact Myris Trade at myris@myris.cz.
