#### Vol. 8, No. 4, 2015

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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
##### Abstract

For the $n$-th order difference equation, ${\Delta }^{n}u=f\left(t,u,\Delta u,\dots ,{\Delta }^{n-1}u,\lambda \right)$, the solution of the boundary value problem satisfying ${\Delta }^{i-1}u\left({t}_{0}\right)={A}_{i},1\le i\le n-1$, and $u\left({t}_{1}\right)-{\sum }_{j=1}^{m}{a}_{j}u\left({\tau }_{j}\right)={A}_{n}$, where ${t}_{0},{\tau }_{1},\dots ,{\tau }_{m},{t}_{1}\in ℤ$, ${t}_{0}<\cdots <{t}_{0}+n-1<{\tau }_{1}<\cdots <{\tau }_{m}<{t}_{1}$, and ${a}_{1},\dots ,{a}_{m},{A}_{1},\dots ,{A}_{n}\in ℝ$, is differentiated with respect to the parameter $\lambda$.

##### Keywords
difference equation, boundary value problem, nonlocal, differentiation with respect to parameters
##### Mathematical Subject Classification 2010
Primary: 39A10, 34B08
Secondary: 34B10