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Existence of strictly decreasing positive solutions of linear differential equations of neutral type. (English) Zbl 1446.34076

A necessary and sufficient condition for the existence of a positive and strictly decreasing solution of the linear neutral differential equation of the form \[ y'(t)=-c(t)y(t-(t))+d(t)y'(t-(t)) \] is established. Comparisons with known results are also given.

MSC:

34K06 Linear functional-differential equations
34K40 Neutral functional-differential equations
34K25 Asymptotic theory of functional-differential equations
34K12 Growth, boundedness, comparison of solutions to functional-differential equations
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