Differentiation with respect to parameters of solutions of nonlocal boundary value problems for difference equations

Henderson, Johnny; Jiang, Xuewei

doi:10.2140/involve.2015.8.629

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Differentiation with respect to parameters of solutions of nonlocal boundary value problems for difference equations

Johnny Henderson and Xuewei Jiang

Vol. 8 (2015), No. 4, 629–636

DOI: 10.2140/involve.2015.8.629

Abstract

For the $n$ -th order difference equation, $Δ^{n} u = f (t, u, Δ u, \dots, Δ^{n - 1} u, λ)$ , the solution of the boundary value problem satisfying $Δ^{i - 1} u (t_{0}) = A_{i}, 1 \leq i \leq n - 1$ , and $u (t_{1}) - \sum_{j = 1}^{m} a_{j} u (τ_{j}) = A_{n}$ , where $t_{0}, τ_{1}, \dots, τ_{m}, t_{1} \in ℤ$ , $t_{0} < \dots < t_{0} + n - 1 < τ_{1} < \dots < τ_{m} < t_{1}$ , and $a_{1}, \dots, a_{m}, A_{1}, \dots, A_{n} \in ℝ$ , is differentiated with respect to the parameter $λ$ .

Keywords

difference equation, boundary value problem, nonlocal, differentiation with respect to parameters

Mathematical Subject Classification 2010

Primary: 39A10, 34B08

Secondary: 34B10

Milestones

Received: 12 May 2014

Revised: 21 May 2014

Accepted: 31 May 2014

Published: 23 June 2015

Communicated by Kenneth S. Berenhaut

Authors

Johnny Henderson
Department of Mathematics Baylor University One Bear Place #97328 Waco, TX 76798 United States

Xuewei Jiang
Department of Mathematics Baylor University One Bear Place #97328 Waco, TX 76798 United States

Vol. 8, No. 4, 2015