Positivity of the Green Functions for Higher Order Ordinary Differential Equations
نویسنده
چکیده
We consider the equation n X k=0 ak(t)x (n−k)(t) = 0, t ≥ 0, where a0(t) ≡ 1, ak(t) (k = 1, . . . , n) are real bounded functions. Assuming that all the roots of the polynomial zn+a1(t)zn−1+· · ·+an(t) (t ≥ 0) are real, we derive positivity conditions for the Green function for the Cauchy problem. We also establish a lower estimate for the Green function and a comparison theorem for solutions.
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تاریخ انتشار 2008