A Singular Singularly-Perturbed Linear Boundary Value Problem.

摘要

The asymptotic solution of boundary value problems are considered for the vector system dx/dt = A(t, epsilon)x + B(t, epsilon)y + C(t, epsilon, epsilon dy/dt = E(t, epsilon)x + F(t, epsilon)y + G(t, epsilon) as epsilon approaches 0 under the assumption that the matrix F(t,0) is singular. A full set of asymptotic solutions is constructed assuming that F(t,0) can be block-diagonalized, the reduced problem is consistent, and a new stability condition holds. Boundary value problems are then solvable if an appropriate 'boundary' matrix is nonsingular for epsilon not = 0. Such problems arise in optimal control theory, among other applications.