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Zbl 0833.35144
Gopalsamy, K.; He, Xuezhong; Sun, Daqing
Oscillations in a delay logistic equation with diffusion. (English)
[A] Agarwal, R. P. (ed.), Recent trends in differential equations. Singapore: World Scientific Publishing. World Sci. Ser. Appl. Anal. 1, 239-252 (1992). ISBN 981-02-0963-0

Summary: Sufficient conditions are obtained for all positive solutions of the diffusive delay-logistic equation $${\partial N(x, t)\over \partial t}= D {\partial^2 N(x, t)\over \partial x^2}+ rN(x, t)\Biggl[1- {N(x, t- \tau)\over K}\Biggr];\quad t> 0, x\in (0, \ell),$$ $$N(x, t)= K\qquad\text{for}\quad x= 0,\quad x= \ell\quad\text{and}\quad t\ge - \tau$$ to be oscillatory about the positive equilibrium.

MSC 2000:: *35R10 Difference-partial differential equations
35B05 General behavior of solutions of PDE
92D25 Population dynamics
34K10 Boundary value problems for functional-differential equations

Keywords: logistic equation; population dynamics

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