The Solvability of the Discrete Boundary Value Problem on the Half-Line

This paper provides conditions for the existence of a solution to the second-order nonlinear boundary value problem on the half-line of the form Δa(n)Δx(n)=f(n+1,x(n+1),Δx(n+1)),n∈N∪{0}, with αx(0)+βa(0)Δx(0)=0,x(∞)=d, where d,α,β∈R, α2+β2>0. To achieve our goal, we use Schauder’s fixed-point the...

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Bibliographic Details
Published in:Entropy (Basel, Switzerland) Switzerland), 2021-11, Vol.23 (11), p.1526
Main Author: Nockowska-Rosiak, Magdalena
Format: Article
Language:English
Subjects:
Banach spaces
Boundary value problems
discrete boundary value problem on infinite interval
Fixed points (mathematics)
fixed-point theorem
Fredholm operator of index 0
Ordinary differential equations
Perturbation methods
perturbation technique
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Summary:This paper provides conditions for the existence of a solution to the second-order nonlinear boundary value problem on the half-line of the form Δa(n)Δx(n)=f(n+1,x(n+1),Δx(n+1)),n∈N∪{0}, with αx(0)+βa(0)Δx(0)=0,x(∞)=d, where d,α,β∈R, α2+β2>0. To achieve our goal, we use Schauder’s fixed-point theorem and the perturbation technique for a Fredholm operator of index 0. Moreover, we construct the necessary condition for the existence of a solution to the considered problem.
ISSN:1099-4300
1099-4300
DOI:10.3390/e23111526