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impulsive equation; nonlocal boundary value problem; Green's function; positivity of Green's function; negativity of Green's function; estimates of solutions
We propose results about sign-constancy of Green's functions to impulsive nonlocal boundary value problems in a form of theorems about differential inequalities. One of the ideas of our approach is to construct Green's functions of boundary value problems for simple auxiliary differential equations with impulses. Careful analysis of these Green's functions allows us to get conclusions about the sign-constancy of Green's functions to given functional differential boundary value problems, using the technique of theorems about differential and integral inequalities and estimates of spectral radii of the corresponding compact operators in the space of essential bounded functions.
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