Existence of solutions to higher-order discrete three-point problems
Anderson, Douglas R.
Southwest Texas State University, Department of Mathematics
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.
Difference equations, Boundary-value problem, Green's function, Fixed points, Cone
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.