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Proceedings of the American Mathematical Society

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A Sturm-Liouville theorem for some odd multivalued maps


Authors: Jo ao-Paulo Dias and Jesús Hernández
Journal: Proc. Amer. Math. Soc. 53 (1975), 72-74
MSC: Primary 47H99; Secondary 47A99
DOI: https://doi.org/10.1090/S0002-9939-1975-0377632-8
MathSciNet review: 0377632
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Abstract: Let $ T:H \to {2^H}$ be the subdifferential of a real l. s. c. convex function on an infinite dimensional, separable, real Hilbert space $ H$. Assuming that $ T$ is odd (i.e. $ T( - u) = - Tu,\;\forall u\;\epsilon H)$), $ 0\epsilon T(0),\;{(I + T)^{ - 1}}$ is compact and $ T(0)$ satisfies a geometrical condition, we prove that $ T$ has an infinite sequence $ \{ {\lambda _n}\} $ of eigenvalues such that $ 0 \leqslant {\lambda _{n\,\overrightarrow n }} + \infty $.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0377632-8
Keywords: Subdifferential, maximal monotone operator, genus of a closed symmetric subset, Sobolev spaces
Article copyright: © Copyright 1975 American Mathematical Society