About Positivity of Green's Functions for Nonlocal Boundary Value Problems with Impulsive Delay Equations

الملخص EN

The impulsive delay differential equation is considered ( L x ) ( t ) = x ′ ( t ) + ∑ i = 1 m p i ( t ) x ( t - τ i ( t ) ) = f ( t ) , t ∈ [ a , b ] , x ( t j ) = β j x ( t j - 0 ) , j = 1 , … , k , a = t 0 < t 1 < t 2 < ⋯ < t k < t k + 1 = b , x ( ζ ) = 0 , ζ ∉ [ a , b ] , with nonlocal boundary condition l x = ∫ a b φ s x ′ s d s + θ x a = c , φ ∈ L ∞ a , b ; θ , c ∈ R .

Various results on existence and uniqueness of solutions and on positivity/negativity of the Green's functions for this equation are obtained.