A connection problem involving a logarithmic function

Abstract

A two points connection problem between two sets of fundamental solutions for a system of ordinary differential equations tdX∕dt = (A+tB)X is studied under the assumptions that the eigenvalues λk (k=1, 2, ⋯ , n) of the diagonal matrix B satisfy ∣ λj − λk ∣ > ∣ λk ∣ > 0, and that the matrix A has a pair of congruent eigenvalues. Connection coefficients are calculated by convergent series and error terms are reduced to be asymptotically zero.