Entropy (Nov 2021)

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

  • Magdalena Nockowska-Rosiak

DOI
https://doi.org/10.3390/e23111526
Journal volume & issue
Vol. 23, no. 11
p. 1526

Abstract

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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.

Keywords