Wright's equation has no solutions of period four

DOI10.1017/S0308210500024148zbMath0685.34050OpenAlexW2056191074MaRDI QIDQ4735450

Roger D. Nussbaum

Publication date: 1989

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0308210500024148

zbMATH Keywords

differential-delay equationsnonexistence of periodic solutions

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations (34C10)

Related Items (6)

A general method for computer-assisted proofs of periodic solutions in delay differential problems ⋮ Continuation of solutions and studying delay differential equations via rigorous numerics ⋮ On the construction of periodic solutions of kaplan-yorke type for some differential delay equations ⋮ Hopf bifurcation for Wright-type delay differential equations: the simplest formula, period estimates, and the absence of folds ⋮ Recent advances about the uniqueness of the slowly oscillating periodic solutions of Wright's equation ⋮ An explicit periodic solution of a delay differential equation

Cites Work

• The existence of periodic solutions of \(f'(x)=-\alpha f(x-1)(1+f(x))\)
• Cyclic differential equations and period three solutions of differential- delay equations
• Asymptotic analysis of functional differential equations and solutions of long period
• Global bifurcation of periodic solutions to some autonomous differential delay equations
• Asymptotic estimates for the periods of periodic solutions of a differential-delay equation
• Circulant matrices and differential-delay equations
• Ordinary differential equations which yield periodic solutions of differential delay equations
• On the nonlinear differential delay equation x'(t) = -f(x(t),x(t-1))
• A global bifurcation theorem with applications to functional differential equations
• Periodic solutions of some nonlinear autonomous functional differential equations
• The range of periods of periodic solutions of \(x'(t)=-\alpha f(x(t-1))\)
• Integral averaging and bifurcation
• Global continuation and asymptotic behaviour for periodic solutions of a differential-delay equation
• A periodicity theorem for autonomous functional differential equations
• Periodic solutions of special differential equations: an example in non-linear functional analysis
• A non-linear difference-differential equation.

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