Unbounded and blow-up solutions for a delay logistic equation with\n positive feedback

2017/09/21 by István Győri, Győri, István, Yukihiko Nakata +3
Engineering · Mathematics · Medicine · #34K12 #34K20 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Differential Equations Analysis #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1709.07295

openalex publication_date 2017/09/21 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We study bounded, unbounded and blow-up solutions of a delay logistic\nequation without assuming the dominance of the instantaneous feedback. It is\nshown that there can exist an exponential (thus unbounded) solution for the\nnonlinear problem, and in this case the positive equilibrium is always\nunstable. We obtain a necessary and sufficient condition for the existence of\nblow-up solutions, and characterize a wide class of such solutions. There is a\nparameter set such that the non-trivial equilibrium is locally stable but not\nglobally stable due to the co-existence with blow-up solutions.\n

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