Existence of solutions to higher-order discrete three-point problems
Date
2003-04-15
Authors
Anderson, Douglas R.
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
We are concerned with the higher-order discrete three-point boundary-value problem
(∆n x)(t) = ƒ(t, x(t + θ)), t1 ≤ t ≤ t3 - 1, -τ ≤ θ ≤ 1
(∆ix)(t1) = 0, 0 ≤ i ≤ n - 4, n ≥ 4
α(∆n-3x)(t) - β(∆n-2x)(t) = η(t), t1 - τ - 1 ≤ t ≤ t1
(∆n-2x)(t2) = (∆n-1x)(t3) = 0.
By placing certain restrictions on the nonlinearity and the distance between boundary points, we prove the existence of at least one solution of the boundary value problem by applying the Krasnoselskii fixed point theorem.
Description
Keywords
Difference equations, Boundary-value problem, Green's function, Fixed points, Cone
Citation
Anderson, D. R. (2003). Existence of solutions to higher-order discrete three-point problems. <i>Electronic Journal of Differential Equations, 2003</i>(40), pp. 1-7.