Abstract
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.
Citation
Ralf Bader. Mikhail Kamenskiĭ. Valeri Obukhovskiĭ. "On some classes of operator inclusions with lower semicontinuous nonlinearities." Topol. Methods Nonlinear Anal. 17 (1) 143 - 156, 2001.
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