Some fixed point theorems for multivalued maps and applications (Q1193213)

The topological degree theory for compact multimaps in a Banach space is applied to obtain the domain expansion-compression type and the norm expansion-compression type fixed point theorems generalizing to the multivalued setting the corresponding results of the third author [Nonlinear Anal., Theory Methods Appl. 10, 1293-1302 (1986; Zbl 0613.47052); ``Some fixed point theorems of expansion and compression type with applications'', Nonlinear analysis and applications, Proc. 7th Int. Conf., Arlington/Tex. 1986, Lect. Notes Pure Appl. Math. 109, 213-221 (1987; Zbl 0664.47040)]. Some applications to the eigenvalue problem for compact multimaps and to the boundary problem for parametrized second order differential inclusions and discontinuous differential equations are given. \{Reviewer's remark: Lemma 2 was given earlier in a more general formulation in a paper of \textit{T. D. Davydova} and the reviewer [``On some generalizations of the theorem of Birkhoff-Kellogg-Rothe'' (Russian) in ``Methods of the decision of operator equations'', Voronezh Univ. Press, Voronezh, 38-41 (1978)]\}.