The notion Perron–Frobenius theory usually refers to the interaction between three
properties of operator semigroups: positivity, spectrum and long-time behaviour. These …

We initiate a theory of locally eventually positive operator semigroups on Banach lattices.
Intuitively this means: given a positive initial datum, the solution of the corresponding …

Abstract Consider a C_0 C 0-semigroup (e^ tA) _ t ≥ 0 (e tA) t≥ 0 on a function space or,
more generally, on a Banach lattice E. We prove a sufficient criterion for the operators e^ tA …

An intriguing feature of positive C_0 C 0-semigroups on function spaces (or more generally
on Banach lattices) is that their long-time behaviour is much easier to describe than it is for …

We discuss linear autonomous evolution equations on function spaces which have the
property that a positive initial value leads to a solution which initially changes sign, but then …

Positive $ C_0 $-semigroups that occur in concrete applications are, more often than not,
irreducible. Therefore a deep and extensive theory of irreducibility has been developed that …

Abstract (EN) Combining an idea of Takáč with the techniques of Daners, Glück, and
Kennedy, we investigate individual and uniform (anti-) maximum principles, thereby …

Maximum principles and uniform anti-maximum principles are a ubiquitous topic in PDE
theory that is closely tied to the Krein–Rutman theorem and kernel estimates for resolvents …

We study the evolution equation associated with the biharmonic operator on infinite
cylinders with bounded smooth cross-section subject to Dirichlet boundary conditions. The …

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 …