Continuity with respect to parameter of Green's matrices of multipoint boundary-value problems

Abstract

We investigate a family of parameter-dependent multipoint boundary-value problems for systems of linear ordinary differential equations of order $ r\geq 2$, with the coefficients and right sides belonging to the spaces $(C^{(n-1)})^{m\times m} $ and $(C^{(n-1)})^{m}$ respectively. We find new sufficient conditions under which Green's matrices of these problems are continuous with respect to the parameter.