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Monotone operators. A survey directed to applications to differential equations. (English) Zbl 0724.47025
This is a self-contained and well-written survey on the theory and some applications of monotone operators between a Banach space V and its dual \(V'\). A central point is of course G. J. Minty’s celebrated theorem on the surjectivity of a monotone hemicontinuous coercive operator [Duke Math. J. 29, 341-346 (1962; Zbl 0111.312)] which was respeated later by F. E. Browder [Duke Math. J. 30, 557-566 (1963; Zbl 0119.325)]. Moreover, the author gives a nice scheme on the “hierarchy” between various monotonicity and continuity concepts arising in the theory of monotone operators. The last section is concerned with several applications to both ordinary and partial differential equations, mainly in the spirit of S. Fučik’s and A. Kufner’s book on nonlinear differential equations [Amsterdam (1980; Zbl 0474.35001)]. This paper will be very useful to anyone who wants to get a first orientation on the notions, results, methods, and applications of monotone operators.

47H05 Monotone operators and generalizations
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