A variety of differentiability results for a multi-point boundary value problem
The author establishes differentiability results for the dynamic system \[ x^\Delta=f(t,x),\qquad \sum_{m=1}^k M_m x(t_m)=r, \] where a solution to the system is defined on a time scale \(\mathbb{T}\), \(x^{\Delta}\) is the delta derivative of \(x\), \(r\in \mathbb{R}^n\), and, for each \(1\le m\le k\), \(t_m\in \mathbb{T}\) and \(M_m\) is a constant \(n\times n\)-matrix. The results obtained unify the corresponding work in the real and the discrete case.
scientific article; zbMATH DE number 1758482