English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

Let X be a real, reflexive, locally uniformly convex Banach space with X* locally uniformly convex. Let T: X D D(T) -4 2X be a maximal monotone operator and G C X open and bounded. Assume that M C X* is pathwise connected and such that T(D(T) n G) n M + 0 and T(D(T) n oG) n M = 0. Then M C T(D(T) n G). If, moreover, T is of type (S) on o9G, then T(D(T) n 9G) may be replaced above by T(D(T) n 9G). The significance of this result lies in the fact that it holds for multi-valued mappings T which do not have to satisfy intD(T) -0. It has also been used in this paper in order to establish a general "invariance of domain" result for maximal monotone operators, and may be applied to a greater variety of problems involving partial differential equations. No degree theory has been used. In addition to the above, necessary and sufficient conditions are given for the existence of a zero (in an open and bounded set G) of a completely continuous perturbation T + C of a maximal monotone operator T such that T + C is locally monotone on G.

An invariance of domain result for multi-valued maximal monotone operators whose domains do not necessarily contain any open sets