Existence of solutions to higher-order discrete three-point problems

Date

2003-04-15

Authors

Anderson, Douglas R.

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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.

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Attribution 4.0 International

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