On the global attractivity and oscillations in a class of second order difference equations from macroeconomics

2010/02/16 by Hassan A. El-Morshedy, El-Morshedy, Hassan A.
Mathematics · #39A10 #39A11 #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #math.CA #math.DS #msc:39A10 #msc:39A11

paper · pdf · doi:10.48550/arxiv.1002.3090

the final version of this paper will be published in Journal of Difference Equations and Applications

arxiv created 2010/02/16 · arxiv updated 2010/02/26

Abstract

New global attractivity criteria are obtained for the second order difference equation x_n+1=cx_n+f(x_n-x_n-1), n=1, 2, ... via a Lyapunov-like method. Some of these results are sharp and support recent related conjectures. Also, a necessary and sufficient condition for the oscillation of this equation is obtained using comparison with a second order linear difference equation with positive coefficients.

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