Resumen de Asymptotic Behavior of Solutions to Difference Equations of Neutral Type
Magdalena Nockowska Rosiak, Janusz Migda
We present sufficient conditions for the existence of a solution x to an equation m(xn − un xn−k ) = an f (xn−τ ) + bn, which is “close” to a given solution y to the linear homogeneous equation of neutral type m(yn − λyn−k ) = 0, where λ is the limit of the sequence u. Closeness of solutions to above equations is understood as xn − yn = o(ωn), where ω is a given nonincreasing sequence with positive values. Moreover, we establish under which conditions for a given solution x to m(xn − un xn−k ) = an f (xn−τ ) + bn and a given nonincreasing sequence with positive values ω there exists a polynomial sequence ϕ of degree less than m such that xn = ϕ(n) + o(ωn). Presented conditions strongly depend on λ.
