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http://dx.doi.org/10.4134/BKMS.2004.41.3.435

h-STABILITY FOR NONLINEAR PERTURBED DIFFERENCE SYSTEMS  

Choi, Sung-Kyu (Department of Mathematics, Chungnam National University)
Koo, Nam-Jip (Department of Mathematics, Chungnam National University)
Song, Se-Mok (Department of Mathematics Education, Chongju University)
Publication Information
Bulletin of the Korean Mathematical Society / v.41, no.3, 2004 , pp. 435-450 More about this Journal
Abstract
We show that two concepts of h-stability and h-stability in variation for nonlinear difference systems are equivalent by using the concept of $n_{\infty}$-summable similarity of their associated variational systems. Also, we study h-stability for perturbed non-linear system y(n+1) =f(n,y(n)) + g(n,y(n), Sy(n)) of nonlinear difference system x(n+1) =f(n,x(n)) using the comparison principle and extended discrete Bihari-type inequality.
Keywords
$n_{\infty}$-summable similarity; h-system; Bihari-type inequality; comparison principle;
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