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math.AP2025
Variational solutions of the Dirichlet problem, Lebesgue's cusp and non-local properties
Wolfgang Arendt, Daniel Daners, Manfred Sauter
A recent result from [AtES24] allows one to define variational solutions of the Dirichlet problem for general continuous boundary data. We establish basic properties of this notion…
math.AP2024
Semi-linear evolution equations via positive semigroups
Wolfgang Arendt, Daniel Daners
We study semi-linear evolutionary problems where the linear part is the generator of a positive -semigroup. The non-linear part is assumed to be quasi-increasing. Given an ini…
math.AP2024
Logistic growth in seasonally changing environments
Daniel Daners, Zeaiter Zeaiter
We consider a parameter dependent periodic-logistic problem with a logistic term involving a degeneracy that replicates time dependent refuges in the habitat of a population. Worki…