Singularly Perturbed Equations

Let us show that the same results are valid for singularly perturbed differential operators with periodic or almost periodic coefficients for sufficiently small values of parameter ε.

Consider a singularly perturbed differential operator

L(ε)x = ε dx

dt −A(t)x, (8.1)

where ε > 0 is a small parameter, A(t) is a square matrix of order n with its elements being almost periodic functions.