Solutions of \(n\)-point boundary value problems associated with nonlinear summary difference equations (Q1360157)

Systems of nonlinear difference equations \(\Delta v(k)=f(k,v(k),\sum^{k-1}_{i=k_0} a(k,i,v(i))\) are considered subject to an \(n\)-point condition \(A_1v(k_1)+\dots+A_n v(k_n)=\gamma\), where \(v\) and \(\gamma\) are \(m\)-dimensional vectors, and \(A_i\) corresponding matrices. Existence and uniqueness of the solution in generalized normed spaces are proved by means of new variation of parameter formulae. The solutions are also approximated iteratively, and numerical results are given.