Roberto Conti (23 April 1923 – 30 August 2006) was an Italian mathematician, who contributed to the theory of ordinary differential equations and the development of the comparison method.

Biography

Roberto Conti was born in Florence on 29 April 1923. He obtained his M.Sc. and Ph.D. in mathematics from the Scuola Normale Superiore di Pisa, under the supervision, respectively, of Leonida Tonelli (replaced, after his premature death, by Emilio Baiada) and Giovanni Sansone. Conti’s M.Sc. and Ph.D. dissertations dealt with translation surfaces (possibly a topic suggested by Tonelli after knowing about some Russian works) and particular aspects of the Cauchy problem. Later he held the position of research assistant to the chair of Sansone at the University of Florence. Their collaboration was fruitful and resulted in numerous articles, as well as the book (Sansone & Conti 1964),(Sansone & Conti 1964) originally published in Italian, which was translated into a number of languages and became one of the standard texts on the subject in the 1960s. In 1956 Conti became full professor at the University of Catania, holding the chair of mathematical analysis until 1958, when he returned to Florence. In 1963-1964 he held a visiting professorship at the Research Institute for Advanced Studies (RIAS) in Baltimore, Maryland.[citation needed]

His research focused on several topics, which often overlapped in the time and contributed to motivate each other. A leading theme was constituted by functional analysis and its applications to the theory of ordinary differential equations, dynamical systems and control systems. An impulse to do research on control systems was most probably given by his discussions with the Russian engineer and mathematician Nicolas Minorsky, who first proposed application of control theory to the automatic steering of ships. Minorsky, after the Russian Revolution, moved to U.S. and later to southern France: during that period he came frequently to Florence, to give seminars and exchange mathematical ideas with Sansone and Conti. On another hand, Conti’s contributions to the development of the comparison method for the qualitative analysis of differential equations were particularly prominent. He was a corresponding member of the Accademia dei Lincei since 1983 and a full member since 1994, a foreign honorary member of the Romanian Academy since 1997 and was also a member of the editorial board of the Journal of Differential Equations since its inception in 1964 until his death in 2006.

Selected works

Books and book chapters

  • Sansone, Giovanni; Conti, Roberto (1956), Equazioni differenziali non lineari, Monografie matematiche del Consiglio Nazionale delle Ricerche (in Italian), vol. 3, Roma: Edizioni Cremonese, pp. XIX+647, MR , Zbl, translated in English as Sansone, Giovanni; Conti, Roberto (1964), (PDF), International Series of Monographs in Pure and Applied Mathematics, vol. 67, translated by Diamond, Ainsley H., Oxford–London–Edinburg–New York–Paris–Frankfurt: Pergamon Press, pp. XIII+533, ISBN 978-0080101941, MR , Zbl , archived from (PDF) on 1 July 2016 {{citation}}:ISBN / Date incompatibility (help)
  • Reissig, Rolf; Sansone, Giovanni; Conti, Roberto (1964), Qualitative Theorie nichtlineare Differentialgleichungen [Qualitative Theory of Nonlinear Differential Equations] (in German), Roma: Edizioni Cremonese, pp. XXXII+382, MR , Zbl.
  • Reissig, Rolf; Sansone, Giovanni; Conti, Roberto (1969), Nichtlineare Differentialgleichungen höherer Ordnung, Monografie matematiche del Consiglio Nazionale delle Ricerche (in German), vol. 16, Roma: Edizioni Cremonese, pp. XV+738, MR , Zbl, translated in English as Reissig, Rolf; Sansone, Giovanni; Conti, Roberto (1974), Non-linear differential equations of higher order, Monographs and Textbooks on Pure and Applied Mathematics, Leyden: Noordhoff International Publishing, pp. xiii+669, ISBN 90-01-75270-5, MR , Zbl.
  • Conti, Roberto (1977), Problemi di Controllo e di Controllo Ottimale, Collezione di matematica applicata (in Italian), vol. 6 (3 ed.), Turin: Unione Tipografico-Editrice Torinese, p. 239, ISBN 9788802019468
  • Conti, Roberto (1977), Linear Differential Equations and Control, Institutiones Mathematicae, vol. 1, Rome / London–New York: Istituto Nazionale di Alta Matematica / Academic Press, p. 174, ISBN 978-0123636010, MR , Zbl.
  • Conti, Roberto; Galeotti, Marcello (2000), "Chapter 2: Totally Bounded Cubic Systems in ℝ2", in Macki, J. W.; Zecca, P. (eds.), Dynamical Systems. Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 19-26, 2000, Lecture Notes in Mathematics, vol. 1822, Springer, pp. 103–172, doi:, ISBN 3-540-40786-3, MR , Zbl.

Articles

  • Conti, Roberto (1955), [On the stability of systems of linear differential equations] (PDF), Rivista di Matematica della Università di Parma, (1) (in Italian), 6: 5–35, MR , Zbl.
  • Conti, Roberto (1956), ["Amplitude" limitations of the solutions to a system of differential equations and their applications], Bollettino dell'Unione Matematica Italiana, Serie III (in Italian), 11 (3): 334–349, MR , Zbl.
  • Conti, Roberto (1956a), [On the continuability of solutions to a system of ordinary differential equations], Bollettino dell'Unione Matematica Italiana, Serie III (in Italian), 11 (4): 510–514, MR , Zbl.
  • Conti, Roberto (1957), [On the t∞–similitude between matrices and the asymptotic equivalence of linear differential systems] (PDF), Rivista di Matematica della Università di Parma, (1) (in Italian), 8: 43–47, MR , Zbl.
  • Conti, Roberto (1965), "Contributions to linear control theory", Journal of Differential Equations, 1 (4): 427–445, Bibcode:, doi:, MR , Zbl
  • Conti, Roberto (1966), (PDF), Funkcialaj Ekvacioj, 9: 23–26, MR , Zbl.
  • Conti, Roberto (1967), , Bollettino dell'Unione Matematica Italiana, Serie III, 22 (2): 135–178, MR , Zbl
  • Conti, Roberto (1968), "On ordinary differential equations with interface conditions", J. Differential Equations, 4 (1): 4–11, Bibcode:, doi:.
  • Conti, Roberto (1983), "Return sets of a linear control process", J. Optim. Theory Appl., 41 (1): 37–53, doi:, ISSN , S2CID.
  • Conti, Roberto (1991), (PDF), Rivista di Matematica della Università di Parma, (4), 17: 217–220, MR , Zbl.
  • Conti, Roberto (1998), , Le Matematiche, 53 (2): 207–240, MR , Zbl.
  • Conti, Roberto; Galeotti, Marcello (2002), , Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Serie IX, 13 (2): 91–99, MR , Zbl.

Notes

  • Accademia Nazionale dei Lincei (2012), (PDF) (in Italian), Roma: Accademia Nazionale dei Lincei, p. 734. The "Yearbook" of the renowned Italian scientific institution, including an historical sketch of its history, the list of all past and present members as well as a wealth of information about its academic and scientific activities.
  • Corduneanu, Constantin (2009), , Libertas Mathematica, XXIX: 113–116, MR , Zbl.
  • Marino, Mario (2008), [In memory of Prof. Giuseppe Santagati], Bollettino dell'Accademia Gioenia (in Italian), 41 (369): 1–7[dead link].
  • Bacciotti, Andrea; Pandolfi, Luciano (2007), (PDF), Bollettino della Unione Matematica Italiana, Sezione A, la Matematica Nella Società e Nella Cultura (in Italian), 8 (16–A), Dipartimento di Scienze Matematiche "Giuseppe Luigi Lagrange", Polytechnic University of Turin: 585–602.
  • Villari, Gabriele Jr. (2007), , Journal of Differential Equations, 234 (1): 337–338, doi:, MR , Zbl.

External links