Mathematics Faculty Articles
A Difference Equation with Anti-Periodic Boundary Conditions
Document Type
Article
Publication Date
1-1-2015
Publication Title
Dynamics of Continuous, Discrete and Impulsive Systems, Series A: Mathematical Analysis
Keywords
Fixed Point Theorem, Difference Equation, Antiperiodic, Antisymmetric, Functional
ISSN
1201-3390
Volume
22
Issue/No.
1
First Page
47
Last Page
60
Abstract
In this paper, we apply an extension of the Leggett-Williams fixed point theorem to the second order difference equation ∆2u(k)+f(u(k+1)) = 0, k ∈ {0, 1, . . . , N}, satisfying the anti-periodic boundary conditions u(0) + u(N + 2) = 0, ∆u(0) + ∆u(N +1) = 0. Two important results of this paper involve providing the Green’s function for −∆2u(k) = 0 satisfying u(0) + u(N + 2) = 0, ∆u(0) + ∆u(N + 1) = 0 and showing this Green’s function satisfies a concavity like property. An example is also given.
NSUWorks Citation
Lyons, Jeffrey W. and Neugebauer, Jeffrey T., "A Difference Equation with Anti-Periodic Boundary Conditions" (2015). Mathematics Faculty Articles. 19.
https://nsuworks.nova.edu/math_facarticles/19
Comments
AMS (MOS) subject classification: 39A10.