Asymptotic properties of solutions to difference equations of Sturm–Liouville type

Janusz Migda and Magdalena Nockowska-Rosiak

Applied Mathematics and Computation, 2019, vol. 340, issue C, 126-137

Abstract: We consider the discrete Sturm–Liouville type equation of the form Δ(rnΔxn)=anf(xσ(n))+bn.Assume s is a given nonpositive real number. We present sufficient conditions for the existence of solution x with the asymptotic behavior xn=c(r1−1+⋯+rn−1−1)+d+o(ns)where c, d are given real numbers. Moreover, we establish conditions under which for a given solution x there exist real numbers c, d such that x has the above asymptotic behavior.

Keywords: Sturm–Liouville difference equation; Prescribed asymptotic behavior; Approximation of solution; Bounded solution; Convergent solution (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:340:y:2019:i:c:p:126-137

DOI: 10.1016/j.amc.2018.08.001

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