Generalizations of Browder’s degree theory

Hu, Shou Chuan; Papageorgiou, Nikolaos S.

doi:10.1090/S0002-9947-1995-1284911-6

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: 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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