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Square-summable stability in parabolic Volterra difference equations
1996
Methods and Applications of Analysis
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We consider some linear and nonlinear parabolic Volterra difference equations of the forms (OO s oo Um,n -2^ < ij u m,n-rj J + ^JPt^m.n-fci = R^lUm-l,n+l j=l ' i=l and OO -] oo A2 h (Um,n) -Y^qjgiUm^n-rj) + Yl Pif^m^n-ki ) = RAiF(Um-l,n+l) '-i=l -I t=l for 771 = 0,1,..., M-1 and n = 0,1,..., and we obtain several sufficient conditions for the square-summable stability and ^-square-summable stability of the zero solution.
doi:10.4310/maa.1996.v3.n2.a7
fatcat:d4ibwufzgje5daq6bm4bwr6d64