Existence of a non-constant periodic solution of a non-linear autonomous functional differential equation representing the growth of a single species population
- 1 September 1975
- journal article
- research article
- Published by Springer Nature in Journal of Mathematical Biology
- Vol. 1 (3) , 227-240
- https://doi.org/10.1007/bf01273745
Abstract
Summary We consider an integro-differential equation for the densityn of a single species population where the birth rate is constant and the death rate depends on the values ofn in an interval of length τ — 1 > 0. We prove the existence of a non-constant periodic solution under the conditions birth rate b > π/2 and τ- 1 small enough. The basic idea of proof (due to R. D. Nussbaum) is to employ a theorem about non-ejective fixed points for a translation operator associated with the solutions of the equation.Keywords
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