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Integral inclusions of upper semi-continuous or lower semi-continuous type. (English) Zbl 0860.45007
The author establishes existence results for Volterra inclusions of the form $y(t) \in \int^t_0 k(t,s)F \bigl(s,y(s)\bigr) ds+g(t), \quad t \in[0,T],$ and for Hammerstein inclusions of the form $y(t)\in \int^T_0k(t,s) F\bigl(s,y(s) \bigr)ds + g(t), \quad t \in[0,T].$ Here $$F$$ is a multivalued function with nonempty compact values and $$F$$ satisfies certain other conditions which are shown to imply either lower or upper semi-continuity for certain related mappings. The kernel $$k$$ is assumed to be essentially bounded. The proofs rely on fixed-point theorems. Some of the results for superlinear inclusions are new even for integral equations.

##### MSC:
 45G10 Other nonlinear integral equations
Full Text:
##### References:
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