On some classes of operator inclusions with lower semicontinuous nonlinearities
Keywords
Multivalued map, topological degree, measure of noncompactness, differential inclusionAbstract
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.Downloads
Published
2001-03-01
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1.
BADER, Ralf, KAMENSKIĬ, Mikhail I. and OBUKHOVSKIĬ, Valeri. On some classes of operator inclusions with lower semicontinuous nonlinearities. Topological Methods in Nonlinear Analysis. Online. 1 March 2001. Vol. 17, no. 1, pp. 143 - 156. [Accessed 7 February 2025].
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