On boundary value problems for systems of linear generalized ordinary differential equations with singularities (Q2461873)

The author studies the existence of a solution for the system of linear generalized ordinary differential equations: \[ \begin{cases} dx_{i}=dA_{i1}x_{1}( t) +dA_{i2}x_{2}( t) +df_{i}( t), \\ l_{i}( x_{1},x_{2}) =c_{i}\qquad \text{for }i=1,2, \end{cases} \] where \(A_{ik}\in \text{BV}([ a,b], \mathbb{R} ^{n_{i}\times n_{k}}) \) and \(f_{i}\in \text{BV}([ a,b] , \mathbb{R} ^{n_{i}}) \) for \(i,k\in\{ 1,2\} .\) He considers also another class with the boundary conditions \[ \sum_{k=1}^{m}[ B_{1ik}x_{1ik}( t_{1ik}) +B_{2ik}x_{2ik}( t_{2ik})t] =c_{i},\quad i=1,2, \] where \(B_{jik}\in \mathbb{R} ^{n_{i}\times n_{j}}\) \(( i,j=1,2\); \(k=1,2,\dots,m) .\) He applies known methods for the analysis of singular boundary value problems for systems of ordinary differential equations.