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On the existence of positive solutions for systems of differential equations with a distributed delay. (English) Zbl 1247.34114

Summary: For the system with a distributed delay \[ X'(t)+\sum_{k=1}^m\int_{h_k(t)}^t[d_sR_k(t,s)]X(s)=0 \] sufficient conditions for positivity of the fundamental matrix are obtained. In the case when the fundamental matrix is positive, comparison results and sufficient positivity conditions for solutions are established.

MSC:

34K06 Linear functional-differential equations
45J05 Integro-ordinary differential equations
34K12 Growth, boundedness, comparison of solutions to functional-differential equations
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