Díaz, Lolimar; Naulin, Raúl Variation of constants formulae for difference equations with advanced arguments. (English) Zbl 0982.39008 Int. J. Math. Math. Sci. 24, No. 8, 549-562 (2000). A vector-valued difference equation with advanced arguments \[ y(n+1)= A(n)y(n)+ B(n)y(g(n))+ f(n), \quad g(n)\geq n+1, \] is considered. Under certain assumptions, variation of constants formulas in the form \(y(n)= \Phi(n) \sum_{k=0}^\infty C_k(f)(n)\) are constructed for different sequential spaces where \(\Phi(n)\) denotes the fundamental matrix of the equation \(y(n+1)= A(n)y(n)\) and \(\{C_k\}\) is a sequence of bounded functionals. Reviewer: Quingkai Kong (DeKalb) Cited in 2 Documents MSC: 39A11 Stability of difference equations (MSC2000) Keywords:vector-valued difference equation; advanced arguments; variation of constants formulas; fundamental matrix; bounded functionals PDFBibTeX XMLCite \textit{L. Díaz} and \textit{R. Naulin}, Int. J. Math. Math. Sci. 24, No. 8, 549--562 (2000; Zbl 0982.39008) Full Text: DOI EuDML