Let be a real or complex piecewise-continuous function defined for all values of the real variable and that is periodic with minimum period so that
(1)
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Then the differential equation
(2)
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has two continuously differentiable solutions and , and the characteristic equation is
(3)
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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)
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(5)
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where and are periodic with period (Magnus and Winkler 1979, p. 4).