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Zbl 1186.34092
Kang, Shugui; Shi, Bao; Wang, Genqiang
Existence of maximal and minimal periodic solutions for first-order functional differential equations.
(English)
[J] Appl. Math. Lett. 23, No. 1, 22-25 (2010). ISSN 0893-9659

Summary: One important question in population models is whether periodic solutions exist and whether they are bounded between minimal and maximal solutions. This paper deals with the existence of maximal and minimal periodic solutions for the periodic solutions of a first-order functional differential equation $$y{^{\prime}}(t)= - a(t)y(t)+f(t,y(t - \tau (t)))$$ by using the method of lower and upper solutions.
MSC 2000:
*34K13 Periodic solutions of functional differential equations
47N20 Appl. of operator theory to differential and integral equations

Keywords: first-order functional differential equations; lower and upper solutions; maximal and minimal periodic solutions; existence; fixed point

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