Monatshefte für Mathematik

, Volume 190, Issue 4, pp 769–788 | Cite as

Continuum branch of one-signed periodic solutions of first-order functional equations involving the nonlinearity with zeros

  • Yanqiong LuEmail author
  • Jingjing Wang


In this paper, the authors establish the global structure of one-signed periodic solutions of the first-order functional differential equation
$$\begin{aligned} u'(t)=a(t)u(t)-\lambda f(t,u(t-\tau (t))),\qquad t\in \mathbb {R} \end{aligned}$$
by using unilateral bifurcation theorem, where the nonlinearity \(f\in C(\mathbb {R}\times \mathbb {R},\ \mathbb {R})\) is T-periodic with first variable and having nontrivial zeros, \(a\in C(\mathbb {R},[0,\ \infty ))\) is T-periodic function with \(\int _{0}^{T}a(t)dt>0\), \(\tau \in C(\mathbb {R},\mathbb {R})\) is T-periodic function, \(\lambda >0\) is a parameter.


One-signed periodic solutions Nonlinearity with zeros Functional equations Bifurcation point 

Mathematics Subject Classification

34B15 34K13 34G20 



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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsNorthwest Normal UniversityLanzhouPeople’s Republic of China

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