Topological structure of solution sets of differential inclusions: the constrained case.
Topological and approximation methods of degree theory of set-valued maps
SummaryThe theory of topological degree of set-valued maps determined by morphisms, i.e. maps with values which are continuous images of almost acyclic sets, is presented, together with some of its applications.In the first part, morphisms defined on finite-dimensional Euclidean manifolds are considered and the integer-valued degree is introduced by means of the Eilenberg-Montgomery-Górniewicz method based on the Vietoris-Begle-Sklyarenko theorem and using the approach of Dold in terms of the Alexander-Spanier...
Perron-Frobenius and Krein-Rutman theorems for tangentially positive operators
We study several aspects of a generalized Perron-Frobenius and Krein-Rutman theorems concerning spectral properties of a (possibly unbounded) linear operator on a cone in a Banach space. The operator is subject to the so-called tangency or weak range assumptions implying the resolvent invariance of the cone. The further assumptions rely on relations between the spectral and essential spectral bounds of the operator. In general we do not assume that the cone induces the Banach lattice structure into...
Editors’ preface for the topical issue “Topics in Nonlinear Analysis”
Approximate smoothings of locally Lipschitz functionals
The paper deals with approximation of locally Lipschitz functionals. A concept of approximation, based on the idea of graph approximation of the generalized gradient, is discussed and the existence of such approximations for locally Lipschitz functionals, defined on open domains in , is proved. Subsequently, the procedure of a smooth normal approximation of the class of regular sets (containing e.g. convex and/or epi-Lipschitz sets) is presented.
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