50 citations · 168 across the 13 of their papers we have counts for
8 papers · 1 filter
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…
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…
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…
Semilinear elliptic equations on rough domains
Wolfgang Arendt, Daniel Daners
The paper makes use of recent results in the theory of Banach lattices and positive operators to deal with abstract semilinear equations. The aim is to work with minimal or no regu…
Local uniform convergence and eventual positivity of solutions to biharmonic heat equations
Daniel Daners, Jochen Glück, Jonathan Mui
We study the evolution equation associated with the biharmonic operator on infinite cylinders with bounded smooth cross-section subject to Dirichlet boundary conditions. The focus…
Periodic-parabolic eigenvalue problems with a large parameter and degeneration
Daniel Daners, Christopher Thornett
We consider a periodic-parabolic eigenvalue problem with a non-negative potential vanishing on a non-cylindrical domain satisfying conditions similar to those for the pa…
A Liouville theorem for -harmonic functions on exterior domains
E. N. Dancer, Daniel Daners, Daniel Hauer
We prove Liouville type theorems for -harmonic functions on exterior domains of the -dimensional Euclidean space, where and . We show that every positiv…
On the asymptotic behaviour of the eigenvalues of a Robin problem
Daniel Daners, James B. Kennedy
We prove that every eigenvalue of a Robin problem with boundary parameter on a sufficiently smooth domain behaves asymptotically like as . This generalises…