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Roger David Nussbaum (born 29 January 1944, in Philadelphia) is an American mathematician, specializing in nonlinear functional analysis and differential equations.

Nussbaum graduated in 1965 with a bachelor's degree from Harvard University. He received his Ph.D. in 1969 from the University of Chicago with thesis The Fixed Point Index and Fixed Point Theorems for K-Set Contractions supervised by Felix Browder. At Rutgers University Nussbaum became in 1969 an assistant professor, in 1973 an associate professor, and in 1977 a full professor. He retired there as professor emeritus. He was elected in 2012 a Fellow of the American Mathematical Society.

Selected publications

Articles

• Browder, Felix E.; Nussbaum, Roger D. (1968). "The topological degree for noncompact nonlinear mappings in Banach spaces". Bulletin of the American Mathematical Society. 74 (4): 671–677. doi:10.1090/S0002-9904-1968-11988-3.
• Nussbaum, Roger D. (1969). "The fixed point index and asymptotic fixed point theorems for ${\displaystyle k}$-set-contractions". Bulletin of the American Mathematical Society. 75 (3): 490–496. doi:10.1090/S0002-9904-1969-12213-5.
• —— (1970). "The radius of the essential spectrum". Duke Mathematical Journal. 37 (3): 473–478. doi:10.1215/S0012-7094-70-03759-2.
• —— (1970). "Spectral mapping theorems and perturbation theorems for Browder's essential spectrum". Transactions of the American Mathematical Society. 150 (2): 445–455. doi:10.1090/S0002-9947-1970-0265967-9.
• —— (1971). "The fixed point index for local condensing maps". Annali di Matematica Pura ed Applicata. 89 (1): 217–258. doi:10.1007/BF02414948. ISSN 0373-3114. S2CID 119544692.
• —— (1971). "Some fixed point theorems". Bulletin of the American Mathematical Society. 77 (3): 360–366. doi:10.1090/S0002-9904-1971-12694-0.
• —— (1972). "Some asymptotic fixed point theorems". Transactions of the American Mathematical Society. 171: 349–375. doi:10.1090/S0002-9947-1972-0310719-6.
• —— (1978). "A Hopf global bifurcation theorem for retarded functional differential equations". Transactions of the American Mathematical Society. 238: 139–164. doi:10.1090/S0002-9947-1978-0482913-0.
• —— (1981). "Eigenvectors of nonlinear positive operators and the linear Krein-Rutman theorem". In: Fixed point theory. Lecture Notes in Mathematics. Vol. 886. Berlin; Heidelberg: Springer. pp. 309–330. doi:10.1007/BFb0092191. ISBN 978-3-540-11152-8.
• De Figueiredo D.G.; Lions P.L.; —— (1982). "A Priori Estimates and Existence of Positive Solutions of Semilinear Elliptic Equations". In: Costa D. (ed.) Djairo G. de Figueiredo - Selected Papers. Cham, Switzerland: Springer. pp. 133–155. doi:10.1007/978-3-319-02856-9_11. ISBN 978-3-319-02855-2. (over 600 citations)
• —— (1983). "Some remarks on a conjecture in parameter adaptive control". Systems & Control Letters. 3 (5): 243–246. doi:10.1016/0167-6911(83)90021-X. ISSN 0167-6911. (over 1100 citations)
• ——; Walsh, Bertram (1998). "Approximation by polynomials with nonnegative coefficients and the spectral theory of positive operators". Transactions of the American Mathematical Society. 350 (6): 2367–2391. doi:10.1090/S0002-9947-98-01998-9.
• Mallet-Paret, John; —— (2011). "Inequivalent measures of noncompactness and the radius of the essential spectrum". Proceedings of the American Mathematical Society. 139 (3): 917–930. doi:10.1090/S0002-9939-2010-10511-7.
• ——; Priyadarshi, Amit; Verduyn Lunel, Sjoerd (2012). "Positive operators and Hausdorff dimension of invariant sets". Transactions of the American Mathematical Society. 364 (2): 1029–1066. doi:10.1090/S0002-9947-2011-05484-X.
• Lemmens, Bas; —— (2013). "Continuity of the cone spectral radius". Proceedings of the American Mathematical Society. 141 (8): 2741–2754. arXiv:1107.4532. doi:10.1090/S0002-9939-2013-11520-0.

Books

• with Bas Lemmens: Nonlinear Perron-Frobenius Theory, Cambridge Tracts in Mathematics, Cambridge University Press 2012
• with S. M. Verduyn-Lunel: Generalizations of the Perron-Frobenius Theorem for Nonlinear Maps, Memoirs AMS 1999
• with Heinz-Otto Peitgen: Special and Spurious Solutions of ${\displaystyle {\dot {x}}(t)=-\alpha f(x(t-1))}$, Memoirs AMS, 1984
• with Patrick Fitzpatrick, Jean Mawhin, Mario Martelli: Topological Methods for Ordinary Differential Equations, CIME Lectures, Montecacini Terme 1991, Lecture Notes in Mathematics 1537, Springer Verlag 1993
• Hilbert's projective metric and iterated nonlinear maps, 2 vols., AMS 1988
• Differential-delay equations with two time lags, Memoirs AMS 1978

References

1. biographical information from American Men and Women of Science, Thomson Gale 2004
2. Roger David Nussbaum at the Mathematics Genealogy Project
3. "Roger D. Nussbaum". Mathematics Department, Rutgers University.

• 20th-century American mathematicians
• 21st-century American mathematicians
• Harvard University alumni
• University of Chicago alumni
• Rutgers University faculty
• Fellows of the American Mathematical Society
• 1944 births
• Living people