## On the sign of the Green’s function associated to Hill’s equation with an indefinite potential.(English)Zbl 1161.34014

Summary: We give an $$L^p$$-criterion for the positiveness of the Green’s function of the periodic boundary value problem:
$x''+a(t)x= 0, \quad x(0)= x(T), \quad x'(0)= x'(T)$
with an indefinite potential $$a(t)$$. Moreover, we prove that such Green’s function is negative provided $$a(t)$$ belongs to the image of a suitable periodic Riccati type operator.

### MSC:

 34B27 Green’s functions for ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations
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### References:

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