Abstract
In this work, we make an exhaustive study of the properties of the Green's function related to the periodic boundary value problem L α x ≡ x ″ + a ( t ) x = 0 , x ( 0 ) = x ( T ) , x ′ ( 0 ) = x ′ ( T ) , with a sign-changing potential a(t). Moreover, we obtain new explicit criteria that ensures that the maximum or anti-maximum principle holds for this equation. The given criteria complement previous results in the literature.
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