Paul Rabinowitz

Paul Henry Rabinowitz (* November 15, 1939 in Newark, New Jersey) is an American mathematician who deals with partial differential equations, calculus of variations and dynamic systems.

Life and work

Rabinowitz studied at the Courant Institute of Mathematical Sciences of New York University, where he received his doctorate in 1966 with Jürgen Moser ( Periodic solutions of nonlinear hyperbolic differential equations ). After that he went from January 1966 to 1969 as an Assistant Professor at Stanford University. In 1969 he was an associate professor at the University of Wisconsin- Madison, where he has a full professor since 1971. Since 1986 he has been there, E. B. Van Vleck Professor of Mathematics. He was a visiting professor at Aarhus, at the ETH Zurich (1982, 1994), in Paris ( 1972-1973 ) and in Pisa.

Rabinowitz is known in particular for new results in the study of nonlinear systems. He proved a global Bifurkationstheorem (that is, he proved the existence of a "global" solution branched from the consideration of local, linearized theory). In 1977 he proved the existence of periodic solutions in Hamiltonian systems under the assumption that the energy surface is " star-shaped ". With Michael Crandall, he proved in the 1970s, a sentence about Hopf bifurcations in infinite dimensions.

He developed in the calculus of variations new mini -max methods that can be applied to "indefinite problems " (which do not satisfy the Palais- Smale compactness condition), Rabinowitz, for example, on Hamiltonian systems, semilinear elliptic systems, applied nonlinear wave equations. In 1973 he proved with Antonio Ambrosetti the Mountain Pass Theorem.

1978/79 he was a Guggenheim Fellow. He is a member of the American Academy of Arts and Sciences and an honorary doctorate of the University of Paris ( 1992). In 1984 he was Colloquium Lecturer of the American Mathematical Society ( AMS). In 1998 he received the Birkhoff Prize. In 1978 he was invited speaker at the International Congress of Mathematicians in Helsinki (Critical points of indefinite functionals and periodic solutions of differential equations ). He is a Fellow of the American Mathematical Society.