Numerical-analytic methods for differential-algebraic systems
Sufficient conditions are obtained for existence and uniqueness of solutions of differential-algebraic systems with boundary conditions of the form \[ \begin{gathered} x'=f(t,x,y),\;t\in I=[0, T],\;Ax(0)+Bx(T)=D,\\ y=g(t,x,y),\quad t\in I,\end{gathered} \] where \(f\in C(I\times \mathbb{R}^p\times \mathbb{R}^q,\mathbb{R}^p)\), \(g\in C(I\times \mathbb{R}^p\times \mathbb{R}^q,\mathbb{R}^q)\), and \(A_{p\times p}\), \(B_{p\times p}\) and \(D_{p\times 1}\) are given constant matrices. The numerical-analytic method combined with the comparison method is used to get these results under the assumption that \(f\) and \(g\) satisfy Lipschitz conditions with respect to the last two variables.
scientific article; zbMATH DE number 1822375