Integration of ordinary linear differential equations by Laplace-Stieltjes transforms

Abstract

Let R R be a constant N × N N \times N matrix and g ( t ) g(t) an N × N N \times N matrix of functions representable as absolutely convergent Laplace-Stieltjes transforms for t > 0 t > 0 . The paper gives sufficient conditions for certain solutions of the system y ′ = ( R + g ( t ) ) y y’ = (R + g(t))y to be expressed as Laplace-Stieltjes transforms or as linear combinations of such transforms with coefficients which are powers of t t .