Splitting of two-point boundary problem appearing in the theory of optimal control - Kurina , G. A. (Ukrains’kyi Matematychnyi Zhurnal, 1992)
In a Hilbert space a two-point boundary-value problem is considered that arises during the minimization of a linear quadratic functional on the trajectories of a linear equation with the operator A + εB invertible for sufficiently small ε >0 for the derivative, where A is a Fredholm operator and all B-Jordan chains of the operator A have the same length. It is proved that we can asymptotically split the problem under consideration into a regularly perturbed boundary-value problem and two singularity perturbed Cauchy problems.