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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
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 $.


References [Enhancements On Off] (What's this?)

  • [1] Herbert Amann, Lusternik-Schnirelman theory and non-linear eigenvalue problems, Math. Ann. 199 (1972), 55–72. MR 0350536 (50 #3028)
  • [2] Haïm Brézis, Monotonicity methods in Hilbert spaces and some applications to nonlinear partial differential equations, Contributions to nonlinear functional analysis (Proc. Sympos., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1971) Academic Press, New York, 1971, pp. 101–156. MR 0394323 (52 #15126)
  • [3] -, Opérateurs maximaux monotones et semi-groups de contractions dans les espaces de Hilbert, North-Holland, Amsterdam, 1973.
  • [4] Jo ao-Paulo Dias, Variational inequalities and eigenvalue problems for nonlinear maximal monotone operators in a Hilbert space, Amer. J. Math. 97 (1975), no. 4, 905–914. MR 0420354 (54 #8368)
  • [5] Jo ao-Paulo Dias, Un théorème de Sturm-Liouville pour une classe d’opérateurs non linéaires maximaux monotones, J. Math. Anal. Appl. 47 (1974), 400–405 (French). MR 0367737 (51 #3979)
  • [6] M. A. Krasnosel’skii, Topological methods in the theory of nonlinear integral equations, Translated by A. H. Armstrong; translation edited by J. Burlak. A Pergamon Press Book, The Macmillan Co., New York, 1964. MR 0159197 (28 #2414)
  • [7] Paul H. Rabinowitz, Some aspects of nonlinear eigenvalue problems, Rocky Mountain J. Math. 3 (1973), 161–202. Rocky Mountain Consortium Symposium on Nonlinear Eigenvalue Problems (Santa Fe, N.M., 1971). MR 0320850 (47 #9383)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0377632-8
PII: S 0002-9939(1975)0377632-8
Keywords: Subdifferential, maximal monotone operator, genus of a closed symmetric subset, Sobolev spaces
Article copyright: © Copyright 1975 American Mathematical Society