Asymptotic formulae for nonlinear functional difference equations

✍ Scribed by S. Castillo; M. Pinto

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 327 KB
• Volume: 42
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/s0898-1221(01)00177-8

✦ Synopsis

In this paper, we show asymptotic formulae for solutions of the nonlinear functional difference equation y(n + 1) = L(yn) + V(n, yn) + f(n, Yn), where yn(O) = y(n + O) for 0 • {-r, -r + 1,..., 0}, L, V(n, .) are linear applications, and f(n, .) is not necessarily linear defined from {-r,-r+ 1,... ,0} to C g. We ask for a trichotomic spectral condition on L, IV(n,.)[ ---* 0 as n ---* +oc, [V(n + 1, .) -V(n, .)] • 21, f(n, 0) = 0, and there is "~ • ~1 such that If(n, x) -f(n, y) [ _< "y(n)[x -y[.