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Generalizations of Browder's degree theory


Authors: Shou Chuan Hu and Nikolaos S. Papageorgiou
Journal: Trans. Amer. Math. Soc. 347 (1995), 233-259
MSC: Primary 47H11; Secondary 35J60, 35K55, 47H05, 47N20, 58C30
DOI: https://doi.org/10.1090/S0002-9947-1995-1284911-6
MathSciNet review: 1284911
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Abstract | References | Similar Articles | Additional Information

Abstract: The starting point of this paper is the recent important work of F. E. Browder, who extended degree theory to operators of monotone type. The degree function of Browder is generalized to maps of the form $ T + f + G$, where $ T$ is maximal monotone, $ f$ is of class $ {(S)_ + }$ bounded, and $ G( \cdot )$ is an u.s.c. compact multifunction. It is also generalized to maps of the form $ f + {N_G}$, with $ f$ of class $ {(S)_ + }$ and $ {N_G}$ the Nemitsky operator of a multifunction $ G(x,r)$ satisfying various types of sign conditions. Some examples are also included to illustrate the abstract results.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1995-1284911-6
Keywords: Degree function, monotone operator, operator of class $ {(S)_ + }$, Nemitsky operator, sign condition, multifunction, approximate selector, normalization, additivity on domain, homotopy invariance, compact embedding
Article copyright: © Copyright 1995 American Mathematical Society

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