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Long-time behavior of positive solutions of a differential equation with state-dependent delay

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  • The long-time behavior of positive solutions of a differential equation with state-dependent delay $ \dot{y}(t) = -c(t)y(t-\tau(t,y(t))) $, where $ c $ is a positive coefficient, is considered. Sufficient conditions are given for the existence of positive solutions bounded from below and from above by functions of exponential type. As a consequence, criteria for the existence of positive solutions are derived and their lower bounds are given. Relationships are discussed with the existing results on the existence of positive solutions for delayed differential equations.

    Mathematics Subject Classification: Primary: 34K25; Secondary: 34K12.


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