D. Daners

activity

20092025

most citedEventually Positive Semigroups of Linear Operators

50 citations · 168 across the 13 of their papers we have counts for

collaborators

15 papers

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.SP2025

Positivity properties of the Dirichlet-to-Neumann operator on graphs

Daniel Daners, Jochen Glück, James B. Kennedy

We explore positivity properties of the semigroup generated by the negative of the Dirichlet-to-Neumann operator with real potential $λ$ , defined on a subset of the vertices of a q…

math.AP2024★ 1 cited

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 $C_{0}$ -semigroup. The non-linear part is assumed to be quasi-increasing. Given an ini…

math.AP2024★ 1 cited

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…

math.AP2022★ 3 cited

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…

math.AP2021★ 4 cited

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…

math.FA2019★ 2 cited

An alternative approach to Fréchet derivatives

Shane Arora, Hazel Browne, Daniel Daners

We discuss an alternative approach to Fréchet derivatives on Banach spaces inspired by a characterisation of derivatives due to Carathéodory. The approach allows us to reduce many…

math.FA2018★ 26 cited

A criterion for the uniform eventual positivity of operator semigroups

Daniel Daners, Jochen Glück

Consider a $C_{0}$ -semigroup $(e^{t A})_{t \geq 0}$ on a function space or, more generally, on a Banach lattice $E$ . We prove a sufficient criterion for the operators $e^{t A}$ to be po…

math.FA2017

Towards a perturbation theory for eventually positive semigroups

Daniel Daners, Jochen Glück

We consider eventually positive operator semigroups and study the question whether their eventual positivity is preserved by bounded perturbations of the generator or not. We demon…

math.FA2017★ 19 cited

The role of domination and smoothing conditions in the theory of eventually positive semigroups

Daniel Daners, Jochen Glück

We perform an in-depth study of some domination and smoothing properties of linear operators and of their role within the theory of eventually positive operator semigroups. On the…

math.AP2015★ 13 cited

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 $λm$ vanishing on a non-cylindrical domain $D_{m}$ satisfying conditions similar to those for the pa…

math.FA2015★ 50 cited

Eventually Positive Semigroups of Linear Operators

Daniel Daners, Jochen Glück, James B. Kennedy

We develop a systematic theory of eventually positive semigroups of linear operators mainly on spaces of continuous functions. By eventually positive we mean that for every positiv…

math.FA2015★ 44 cited

Eventually and asymptotically positive semigroups on Banach lattices

Daniel Daners, Jochen Glück, James B. Kennedy

We develop a theory of eventually positive $C_{0}$ -semigroups on Banach lattices, that is, of semigroups for which, for every positive initial value, the solution of the correspondin…

math.AP2014★ 5 cited

A Liouville theorem for $p$ -harmonic functions on exterior domains

E. N. Dancer, Daniel Daners, Daniel Hauer

We prove Liouville type theorems for $p$ -harmonic functions on exterior domains of the $d$ -dimensional Euclidean space, where $1 < p < \infty$ and $d \geq 2$ . We show that every positiv…

math.AP2009

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 $α$ on a sufficiently smooth domain behaves asymptotically like $- α^{2}$ as $α \to \infty$ . This generalises…

Variational solutions of the Dirichlet problem, Lebesgue's cusp and non-local properties

Positivity properties of the Dirichlet-to-Neumann operator on graphs

Semi-linear evolution equations via positive semigroups

Logistic growth in seasonally changing environments

Semilinear elliptic equations on rough domains

Local uniform convergence and eventual positivity of solutions to biharmonic heat equations

An alternative approach to Fréchet derivatives

A criterion for the uniform eventual positivity of operator semigroups

Towards a perturbation theory for eventually positive semigroups

The role of domination and smoothing conditions in the theory of eventually positive semigroups

Periodic-parabolic eigenvalue problems with a large parameter and degeneration

Eventually Positive Semigroups of Linear Operators

Eventually and asymptotically positive semigroups on Banach lattices

A Liouville theorem for p-harmonic functions on exterior domains

On the asymptotic behaviour of the eigenvalues of a Robin problem

A Liouville theorem for $p$ -harmonic functions on exterior domains