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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 bedoi:10.12775/tmna.2001.010 fatcat:tv7a4z3gjze55jmsyw7vcnbomy