Let be a real or complex piecewisecontinuous function defined for all values of the real variable and that is periodic with minimum period so that
(1)

Then the differential equation
(2)

has two continuously differentiable solutions and , and the characteristic equation is
(3)

with eigenvalues and . Then Floquet's theorem states that if the roots and are different from each other, then (2) has two linearly independent solutions
(4)
 
(5)

where and are periodic with period (Magnus and Winkler 1979, p. 4).