On generalized solutions of locally Fuchsian ordinary differential equations

Abstract

We consider an m-th order constant coefficient locally Fuchsian ordinary differential equation at the origin ( ( ) ( ) ( )) ( ) 0 0 0 0, 1 0 1 ∇ + 1 ∇ + + ∇ + = − r − r r y x m m m … where dx d x ∈ R, ∇ = x and prove that there exists generalized solutions to this equation with support on the positive halfline. A long the way, using our method, we establish similar conditions for existence of generalized solutions for a specialized ordinary differential equation proposed in [1]