Asymptotic Integration of Systems of Quasidifferential Equations of Second Order

has already been defined and is locally absolutely continuous, we define the second quasiderivative y σ of the vector function y and the quasidifferential expression l[y] by setting y σ := (y [1] σ ) ′ + σy σ + σ y, l[y](x) := −y σ (x), x ∈ R+. The set D := {y | y, y σ ∈ ACloc(R+)} is the domain of definition of the expression l. Conditions a) and b) imply that, for vector functions y ∈ D, the expression l[y](x) exists a.e., l[y] ∈ Lloc(R+), and, for f, g ∈ D, we have ˆ β