| Abstract: |
| We consider a parameter dependent parabolic logistic population model with diffusion and degenerate logistic term allowing for refuges for the population. The aim is to remove quite restrictive geometric and smoothness conditions on the refuge commonly used. The key is a simplified construction of a supersolution involving a limit theorem for the principal eigenvalue. The method works for non-selfadjoint operators and does not make use of any regularity condition of the refuge. At the same time we also simplify other arguments commonly used in the literature. |
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