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Multiple periodic solutions for a first order nonlinear functional differential equation with applications to population dynamics. (English) Zbl 1187.34092
The existence of periodic solutions for the class of functional differential equations
$y'(t) = -a(t)y(t) +\lambda f(t, y(h(t)))$ is studied, where $$\lambda$$ is a positive parameter and $$h$$, $$a$$, and $$f(\cdot, x)$$ for each $$x\geq 0$$ are nonnegative continuous $$T$$-periodic functions. Sufficient conditions are obtained for the existence of at least three positive periodic solutions by using the Leggett-Williams multiple fixed point theorem. Applications to ecological and population models are also considered.

##### MSC:
 34K13 Periodic solutions to functional-differential equations 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations 34C27 Almost and pseudo-almost periodic solutions to ordinary differential equations 47N20 Applications of operator theory to differential and integral equations 92D25 Population dynamics (general) 92D40 Ecology
##### Keywords:
periodic solutions; functional differential equations