On some classes of operator inclusions with lower semicontinuous nonlinearities

Ralf Bader, Mikhail I. Kamenskiĭ, Valeri Obukhovskiĭ
2001 Topological Methods in Nonlinear Analysis  
We consider a class of multimaps which are the composition of a superposition multioperator 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
more » ... t 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. 2000 Mathematics Subject Classification. 47H11, 47H09, 47H04, 34G25, 34A60.
doi:10.12775/tmna.2001.010 fatcat:tv7a4z3gjze55jmsyw7vcnbomy