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Existence of solutions of nonlinear differential equations via fixed point theorems. (English) Zbl 0581.47040

This paper is the text of a survey lecture given at I.I.T., Madras in 1981. It begins with a selection of general results concerning fixed points of multifunctions and maximal monotone operators. Applications are given to problems in control theory and to linear and non-linear parabolic equations.
In the second part, various problems at resonance are discussed, first in an abstract setting and subsequently in the context of non-linear parabolic and hyperbolic equations.
Reviewer: C.A.Stuart

MSC:

47H05 Monotone operators and generalizations
47H10 Fixed-point theorems
35K25 Higher-order parabolic equations
35L25 Higher-order hyperbolic equations
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