{{short description|American mathematician}} '''Roger David Nussbaum''' (born 29 January 1944, in Philadelphia)<ref>biographical information from ''American Men and Women of Science'', Thomson Gale 2004</ref> 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.<ref>{{MathGenealogyProject|id=6604|title=Roger David Nussbaum}}</ref> 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.<ref>{{cite web|title=Roger D. Nussbaum|website=Mathematics Department, Rutgers University|url=http://www.math.rutgers.edu/~nussbaum/}}</ref> He was elected in 2012 a Fellow of the American Mathematical Society.

==Selected publications== ===Articles=== * {{cite journal|doi=10.1090/S0002-9904-1968-11988-3|title=The topological degree for noncompact nonlinear mappings in Banach spaces|year=1968|last1=Browder|first1=Felix E.|last2=Nussbaum|first2=Roger D.|journal=Bulletin of the American Mathematical Society|volume=74|issue=4|pages=671–677|doi-access=free}} * {{cite journal|doi=10.1090/S0002-9904-1969-12213-5|title=The fixed point index and asymptotic fixed point theorems for <math>k</math>-set-contractions|year=1969|last1=Nussbaum|first1=Roger D.|journal=Bulletin of the American Mathematical Society|volume=75|issue=3|pages=490–496|doi-access=free}} * {{cite journal|author=Nussbaum, Roger D.|author-mask=2|title=The radius of the essential spectrum|journal=Duke Mathematical Journal|volume=37|issue=3|year=1970|pages=473–478|doi=10.1215/S0012-7094-70-03759-2|url=https://projecteuclid.org/journals/duke-mathematical-journal/volume-37/issue-3/The-radius-of-the-essential-spectrum/10.1215/S0012-7094-70-03759-2.short|url-access=subscription}} * {{cite journal|doi=10.1090/S0002-9947-1970-0265967-9|title=Spectral mapping theorems and perturbation theorems for Browder's essential spectrum|year=1970|last1=Nussbaum|first1=Roger D.|author-mask=2|journal=Transactions of the American Mathematical Society|volume=150|issue=2|pages=445–455|doi-access=free}} * {{cite journal|last1=Nussbaum|first1=Roger D.|author-mask=2|title=The fixed point index for local condensing maps|journal=Annali di Matematica Pura ed Applicata|volume=89|issue=1|year=1971|pages=217–258|issn=0373-3114|doi=10.1007/BF02414948|s2cid=119544692 |doi-access=free}} * {{cite journal|doi=10.1090/S0002-9904-1971-12694-0|title=Some fixed point theorems|year=1971|last1=Nussbaum|first1=Roger D.|author-mask=2|journal=Bulletin of the American Mathematical Society|volume=77|issue=3|pages=360–366|doi-access=free}} * {{cite journal|doi=10.1090/S0002-9947-1972-0310719-6|title=Some asymptotic fixed point theorems|year=1972|last1=Nussbaum|first1=Roger D.|author-mask=2|journal=Transactions of the American Mathematical Society|volume=171|pages=349–375|doi-access=free}} * {{cite journal|doi=10.1090/S0002-9947-1978-0482913-0|title=A Hopf global bifurcation theorem for retarded functional differential equations|year=1978|last1=Nussbaum|first1=Roger D.|author-mask=2|journal=Transactions of the American Mathematical Society|volume=238|pages=139–164|doi-access=free}} * {{cite book|author=Nussbaum, Roger D.|author-mask=2|chapter=Eigenvectors of nonlinear positive operators and the linear Krein-Rutman theorem|title=''In:'' Fixed point theory|series=Lecture Notes in Mathematics|pages=309–330|publisher=Springer|location=Berlin; Heidelberg|year=1981|volume=886|doi=10.1007/BFb0092191|isbn=978-3-540-11152-8|chapter-url=https://link.springer.com/chapter/10.1007%2FBFb0092191}} * {{cite book|author=De Figueiredo D.G.|author2=Lions P.L.|author3=Nussbaum R.D.|author-mask3=2|year=1982|chapter=A Priori Estimates and Existence of Positive Solutions of Semilinear Elliptic Equations|title=''In:'' Costa D. (ed.) Djairo G. de Figueiredo - Selected Papers|pages=133–155 |publisher=Springer|location=Cham, Switzerland|doi=10.1007/978-3-319-02856-9_11 |isbn=978-3-319-02855-2 |chapter-url=https://doi.org/10.1007/978-3-319-02856-9_11}} (over 600 citations) * {{cite journal|last1=Nussbaum|first1=Roger D.|author-mask=2|title=Some remarks on a conjecture in parameter adaptive control|journal=Systems & Control Letters|volume=3|issue=5|year=1983|pages=243–246|issn=0167-6911|doi=10.1016/0167-6911(83)90021-X}} (over 1100 citations) * {{cite journal|doi=10.1090/S0002-9947-98-01998-9|title=Approximation by polynomials with nonnegative coefficients and the spectral theory of positive operators|year=1998|last1=Nussbaum|first1=Roger D.|author-mask=2|last2=Walsh|first2=Bertram|journal=Transactions of the American Mathematical Society|volume=350|issue=6|pages=2367–2391|doi-access=free}} * {{cite journal|doi=10.1090/S0002-9939-2010-10511-7|title=Inequivalent measures of noncompactness and the radius of the essential spectrum|year=2011|last1=Mallet-Paret|first1=John|last2=Nussbaum|first2=Roger D.|author-mask2=2|journal=Proceedings of the American Mathematical Society|volume=139|issue=3|pages=917–930|doi-access=free}} * {{cite journal|doi=10.1090/S0002-9947-2011-05484-X|title=Positive operators and Hausdorff dimension of invariant sets|year=2012|last1=Nussbaum|first1=Roger D.|author-mask=2|last2=Priyadarshi|first2=Amit|last3=Verduyn Lunel|first3=Sjoerd|journal=Transactions of the American Mathematical Society|volume=364|issue=2|pages=1029–1066|doi-access=free}} * {{cite journal|doi=10.1090/S0002-9939-2013-11520-0|title=Continuity of the cone spectral radius|year=2013|last1=Lemmens|first1=Bas|last2=Nussbaum|first2=Roger|author-mask2=2|journal=Proceedings of the American Mathematical Society|volume=141|issue=8|pages=2741–2754|doi-access=free|arxiv=1107.4532}}

===Books=== *with Bas Lemmens: [https://books.google.com/books?id=EYud2hfi_c4C Nonlinear Perron-Frobenius Theory], Cambridge Tracts in Mathematics, Cambridge University Press 2012 *with S. M. Verduyn-Lunel: [https://books.google.com/books?id=iJnTCQAAQBAJ Generalizations of the Perron-Frobenius Theorem for Nonlinear Maps], Memoirs AMS 1999 *with Heinz-Otto Peitgen: [https://books.google.com/books?id=DzbUCQAAQBAJ Special and Spurious Solutions of <math>\dot{x}(t)=-\alpha f(x(t-1))</math>], 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 *[https://books.google.com/books?id=hV3UCQAAQBAJ Hilbert's projective metric and iterated nonlinear maps], 2 vols., AMS 1988 *[https://books.google.com/books?id=DBDUCQAAQBAJ Differential-delay equations with two time lags], Memoirs AMS 1978

==References== <references/>

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{{DEFAULTSORT:Nussbaum, Roger David}} Category:20th-century American mathematicians Category:21st-century American mathematicians Category:Harvard University alumni Category:University of Chicago alumni Category:Rutgers University faculty Category:Fellows of the American Mathematical Society Category:1944 births Category:Living people