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The linear invariant population evolution equation with time delay. (Chinese. English summary) Zbl 0693.35010

Summary: This paper, by the use of \(C_ 0\)-operator semigroup and the spectrum theory of the operator, discusses the linear invariant population evolution equation with time delay, and presents its asymptotical properties and the sufficient and necessary condition for the stability. We show that when the fertility rate \(\beta\) equals the critical fertility the solution of this equation is oscillatory.

MSC:

35B40 Asymptotic behavior of solutions to PDEs
35R10 Partial functional-differential equations
92D25 Population dynamics (general)
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35B35 Stability in context of PDEs
35G10 Initial value problems for linear higher-order PDEs
35K25 Higher-order parabolic equations
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