On some classes of operator inclusions with lower semicontinuous nonlinearities

Ralf Bader, Mikhail I. Kamenskiĭ, Valeri Obukhovskiĭ

DOI: http://dx.doi.org/10.12775/TMNA.2001.010


We consider a class of multimaps which are the composition of a superposition
multioperator ${\mathcal P}_F$ generated by a nonconvex-valued almost
lower semicontinuous nonlinearity $F$ and an abstract solution operator
$S$. We prove that under some suitable conditions such multimaps are
condensing with respect to a special
vector-valued measure of noncompactness and construct a topological degree
theory for this class of multimaps yielding some fixed point principles. It is
shown how abstract results can be applied to semilinear inclusions,
inclusions with $m$-accretive operators and time-dependent subdifferentials,
nonlinear evolution inclusions and integral inclusions in Banach spaces.


Multivalued map; topological degree; measure of noncompactness; differential inclusion

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