# zbMATH — the first resource for mathematics

Covering dimension and differential inclusions. (English) Zbl 1038.47501
Lower semicontinuous multivalued mappings $$\Phi$$, $$\Psi : X \to 2^Y$$ are considered, where $$X$$, $$Y$$ are Banach spaces. Under some assumptions (closedness and convexity of the values of $$\Phi$$ and $$\Psi$$, surjectivity of $$\Phi$$, a certain compactness of $$\Psi$$, etc.), it is shown that $\dim (\{x \in X;\;\Phi (x) \cap \Psi (x) \neq \emptyset \}) \geq \dim (\Phi ^{-1}(0)),$ where $$\dim$$ denotes the covering dimension. Two applications to differential inclusions are given.
##### MSC:
 47H04 Set-valued operators 26E25 Set-valued functions
Full Text: