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Perturbed Fredholm boundary value problems for delay differential systems. (English) Zbl 1077.34069

The considered linear boundary value problem with a small parameter ε has the form

z ˙(t)= i=1 k A i (t)z(h i (t))+ε i=1 k B i (t)z(h i (t))+g(t),t[a,b];z(s)=ψ(s),s<α;z=α·

The unknown solution z takes values in a finite-dimensional space. The functions h i (t)t are measurable. In case h i (t)<α, it is assumed that z(h i (t))=ψ(h i (t)). The boundary conditions are described by the bounded linear operator . The Fredholm properties of the boundary value problem are obtained in the form of power series in ε. Examples are given.

MSC:
34K10Boundary value problems for functional-differential equations
34K06Linear functional-differential equations