$h$-stability for nonlinear perturbed difference systems
Bull. Korean Math. Soc. 2004 Vol. 41, No. 3, 435-450
Published online September 1, 2004
Sung Kyu Choi, Nam Jip Koo, and Se Mok Song
Chungnam National University, Chungnam National University, Chongju University
Abstract : We show that two concepts of h-stability and h-stabil-ity 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 nonlinear 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
MSC numbers : 39A11
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