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Support functions and subdifferentials

100%
Grzybowski J., Pallaschke D., Urbański R.
Commentationes Mathematicae
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2016
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tom 56
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nr 1
EN
In this paper we study Minkowski duality, i.e. the correspondence between sublinear functions and closed convex sets in the context of dual pairs of vector spaces.
2
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Derivatives of orbital function and an extension of Berezin-Gel’fand’s theorem

86%
Tam T.-Y., Hill W. C.
Special Matrices
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2016
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tom 4
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nr 1
EN
A generalization of a result of Berezin and Gel’fand in the context of Eaton triples is given. The generalization and its proof are Lie-theoretic free and requires some basic knowledge of nonsmooth analysis. The result is then applied to determine the distance between a point and a G-orbit or its convex hull.We also discuss the derivatives of some orbital functions.
3
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Existence and multiplicity results for nonlinear eigenvalue problems with discontinuities

86%
Papageorgiou N. S., Papalini F.
Annales Polonici Mathematici
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2000
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tom 75
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nr 2
125-141
EN
We study eigenvalue problems with discontinuous terms. In particular we consider two problems: a nonlinear problem and a semilinear problem for elliptic equations. In order to study the existence of solutions we replace these two problems with their multivalued approximations and, for the first problem, we estabilish an existence result while for the second problem we prove the existence of multiple nontrivial solutions. The approach used is variational.
4
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Discontinuous quasilinear elliptic problems at resonance

72%
Kourogenis N. C., Papageorgiou N. S.
Colloquium Mathematicum
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1998
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tom 78
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nr 2
213-223
EN
In this paper we study a quasilinear resonant problem with discontinuous right hand side. To develop an existence theory we pass to a multivalued version of the problem, by filling in the gaps at the discontinuity points. We prove the existence of a nontrivial solution using a variational approach based on the critical point theory of nonsmooth locally Lipschitz functionals.
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