Cesari, Lamberto Existence of solutions of nonlinear differential equations via fixed point theorems. (English) Zbl 0581.47040 J. Math. Phys. Sci. 18, 23-41 (1984). 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 Keywords:fixed points of multifunctions; maximal monotone operators; control theory; problems at resonance; non-linear parabolic and hyperbolic equations PDFBibTeX XMLCite \textit{L. Cesari}, J. Math. Phys. Sci. 18, 23--41 (1984; Zbl 0581.47040)