On dichotomy and well-conditioning in two-point boundary-value problems (Q920594)

The boundary value problem \(P(t)y'(t)+Q(t)y(t)=f(t),\quad t\in [a,b]\) \(My(a)+Ny(b)=d,\) where \(M,N\in {\mathbb{R}}^{n\times n}\), \(d\in {\mathbb{R}}^ n\) and \(P,Q\in [L_ p(a,b)]^{n\times n}\), \(f\in [L_ p(a,b)]^ n\), \(1\leq p<\infty\) are given, is considered. The authors investigate the close relationship between the stability constants and the growth behavior of the fundamental matrix of this problem. It is also shown that the conditioning number is the right criterion to indicate possible error amplification of the perturbed boundary conditions.