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

The impulsive delay differential equation is considered(Lx)(t)=x′(t)+∑i=1mpi(t)x(t-τi(t))=f(t), t∈[a,b], x(tj)=βjx(tj-0), j=1,…,k, a=t0<t1<t2<⋯<tk<tk+1=b, x(ζ)=0, ζ∉[a,b],with nonlocal boundary conditionlx=∫abφsx′sds+θxa=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.