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Weak delay in systems with an aftereffect. (English) Zbl 1048.34104

Summary: Systems of linear differential equations with constant coefficients and a constant delay which have a finite number of eigenvalues are considered. Systems in such form are called systems with a weak delay. Necessary and sufficient conditions of a weak delay are obtained. The solution of Cauchy’s task is obtained in explicit form for systems on the plane and for systems in triangular form in three-dimensional space.

MSC:

34K06 Linear functional-differential equations
34K20 Stability theory of functional-differential equations
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