Generalized topological essentiality and coincidence points of multivalued maps (Q833014)

The aim of the paper is to introduce and study the notion of a generalized topological essentiality for a class of set-valued maps in general topological vector spaces satisfying the approximation property known as the Klee admissibility property and, in particular, Fréchet spaces. The so-called \(\Phi\)-essentiality (where \(\Phi\) is a `reference' map that replaces the constant and equals the 0 map in the usual essentiality) of a set-valued map \(\varphi\) serves as the property entailing the existence of coincidences of \(\varphi\) and \(\Phi\). The authors establish the main properties of \(\Phi\)-essential maps. Using inverse systems, the concept of the limit-essentiality is discussed and some applications to systems of differential inclusions subject to asymptotic boundary value conditions on the real half-line are provided.