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Boundary value problems with solutions

Herzog Gerd, Kunstmann Peer Chr.

Opuscula Mathematica

2019

Vol. 39, no. 1

49--60

By means of the continuation method for contractions we prove the existence of solutions of Dirichlet boundary value problems in convex sets. As an application we prove the existence of concave solutions of certain boundary value problems in ordered Banach spaces.

Second order differential inequalities via aggregation

Herzog G., Lemmert R.

Demonstratio Mathematica

2007

Vol. 40, nr 2

347-364

Let E be a Banach space ordered by a solid and normal cone. We introduce a polynorm with respect to a given selection of positive pairwise disjoint vectors p1, . . . , pm, and derive monotonicity properties of solutions of second order differential inequalities under one-sided matrix Lipschitz conditions.

A separation theorem with applications to Edgeworth equivalence in some infinite dimensional setting

Angeloni L., Martellotti A.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2004

Vol. 44, nr 2

227-243

We provide an Edgeworth Equivalence result for a pure exchange economy with a measure space of agents and a separable ordered Banach space as commodity space. In particular, we first establish a necessary and sufficient condition for the Equivalence to hold, by means of an ad hoc separation theorem, which allows us to extend the classical finite-dimensional proof of this result. Our setting does not require nor transitivity neither completeness of preferences. Finally, using the sufficient part of the previous result and assuming negative transitivity of preferences, we show that the Edgeworth Equivalence holds under a suitable properness ([ro]-uniform weak properness) of preferences.