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A functional equation characterizing monomial functions used in permanence theory for ecological differential equations. (English) Zbl 1071.92040
Summary: It is well known that monomial average Lyapunov functions of the form \[ R(x_1,x_2,\dots,x_n)=r_0\prod^n_{i=1}x_i^{r_i}\;(r_k>0,i=0,1,2,\dots,n) \] play an eminent role in the permanence theory of ecological (or Kolmogorov) differential equations. A functional equation characterizing the above class of functions is presented.

MSC:
92D40 Ecology
39B52 Functional equations for functions with more general domains and/or ranges
37N25 Dynamical systems in biology
92D25 Population dynamics (general)
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