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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.

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