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Oscillations in a delay logistic equation with diffusion. (English) Zbl 0833.35144
Agarwal, R. P. (ed.), Recent trends in differential equations. Singapore: World Scientific Publishing. World Sci. Ser. Appl. Anal. 1, 239-252 (1992).
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. For the entire collection see [Zbl 0824.00015].

35R10Partial functional-differential equations
35B05Oscillation, zeros of solutions, mean value theorems, etc. (PDE)
92D25Population dynamics (general)
34K10Boundary value problems for functional-differential equations