Über die Invarianz einer konvexen Menge in bezug auf Systeme von gewöhnlichen, parabolischen und elliptischen Differentialgleichungen.
Über einen Satz von Witte.
Zur Eindeutigkeitsbedingung von Nagumo
Über Endomorphismen mit dichten Bahnen.
Charakterisierungen zeilenendlicher Matrizen mit abzählbarem Spektrum.
Remarks concerning Driver's equation
We consider uniqueness for the initial value problem x' = 1 + f(x) - f(t), x(0) = 0. Several uniqueness criteria are given as well as an example of non-uniqueness.
On quasipositive elements in ordered Banach algebras
Let a real Banach algebra A with unit be ordered by an algebra cone K. We study the elements a ∈ A with exp(ta) ∈ K, t≥ 0.
Positive solutions of systems of boundary value problems.
On BVPs in l(A).
We prove the existence of extremal solutions of Dirichlet boundary value problems for u'' + f(t,u,u') = 0 in l(A) between a generalized pair of upper and lower functions with respect to the coordinatewise ordering, and for f quasimonotone increasing in its second variable.
Second order differential inequalities in Banach spaces
We derive monotonicity results for solutions of ordinary differential inequalities of second order in ordered normed spaces with respect to the boundary values. As a consequence, we get an existence theorem for the Dirichlet boundary value problem by means of a variant of Tarski's Fixed Point Theorem.
Enclosing solutions of second order equations
We apply Max Müller's Theorem to second order equations u'' = f(t,u,u') to obtain solutions between given functions v,w.
On the positivity of semigroups of operators
In a Banach space , let be a -semigroup with generating operator . For a cone with non-empty interior we show: holds if and only if is quasimonotone increasing with respect to . On the other hand, if is not continuous, then there exists a regular cone such that is quasimonotone increasing, but does not hold.
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