Klaus Schmitt

Portrait of Professor Klaus Schmitt

Klaus Schmitt (born 1940 in Rimbach/Odenwald, Germany) is an American mathematician doing research in nonlinear differential equations, and nonlinear analysis.

Schmitt completed the Abitur at Rimbach's Martin-Luther-Schule in 1960. He received a BA in mathematics and physics from St. Olaf College in 1962, an MA (1964) and PhD in mathematics from the University of Nebraska in 1967. He began his 43-year career at the University of Utah in 1967, first as assistant, then associate, then as full professor of mathematics. He also served as chairman of the department of mathematics from 1989 to 1992.

Schmitt served short-term appointments as visiting professor at the University of Würzburg,  University of Karlsruhe, University of Stuttgart, University Catholique de Louvain, University of Bremen, Technische Universität Berlin, University of Heidelberg, University of Kaiserslautern, University of Sydney, Universidad de Chile, Universidad Catolica de Chile, National Chengchi University in Taiwan, National Tsing Hua University in Taiwan and the Chern Institute of Mathematics in Tianjin, China.

He has served as professor emeritus of mathematics at the University of Utah since 2010.

Schmitt was awarded the Humboldt Prize in mathematics in 1978 and was honored as a University of Nebraska Distinguished Alumnus in 2000.

Selected publications

• "Boundary value problems for quasilinear elliptic partial differential equations", Nonlinear Analysis, 2 (1978), 263-309. ^[1]
• "Nonlinear elliptic boundary value problems versus their finite difference approximations: Numerically irrelevant solutions" (with H.O. Peitgen and D. Saupe), Journal für die reine und angewandte Mathematik (Crelle's Journal), 322 (1981), 74-117. ^[2]
• "Global analysis of elliptic two parameter eigenvalue problems" (with H.O. Peitgen), Transactions of the American Mathematical Society , 283(1984), 57-95. ^[3]
• "Global aspects of the discrete and continuous Newton method: A case study" (with H.O. Peitgen and M. Prüfer), Acta Applicandae Mathematicae , 13 (1988), 123-202. ^[4]
• "On positive solutions of semilinear elliptic equations" (with E.N. Dancer), Proceedings of the American Mathematical Society , 101 (1987), 445-452. ^[5]
• "Permanence and dynamics in biological systems" (with V. Hutson), Mathematical Biosciences , 111 (1992), 1-71. ^[6]
• "Landesman-Lazer type problems at an eigenvalue of odd multiplicity" (with J. Mawhin), Results in Mathematics , 14 (1988), 138-146. ^[7]
• "Positive solutions and conjugate points for systems of differential equations" (with H. Smith), Nonlinear Analysis: Theory, Methods & Applications, 2 (1978), 93-105. ^[8]
• "Asymptotic behavior of positive solution branches of semilinear elliptic problems with linear part at resonance" (with R. Schaaf), Zeitschrift für Angewandte Mathematik und Physik , 43 (1992), 645-676. ^[9]
• "Minimization problems for noncoercive functionals subject to constraints" (with V. K. Le), Transactions of the American Mathematical Society, 347 (1995), 4485-4513. ^[10]
• Global Bifurcation in Variational Inequalities: Applications to Obstacle and Unilateral Problems (with L. K. Vy), vol 123, Applied Mathematical Sciences, Springer Verlag, New York, 1997. ^[11]
• "Mountain pass type solutions of quasilinear elliptic equations" (with P. Clément, M. García-Huidobro, and R. Manásevich), Calculus of Variations and Partial Differential Equations, 11 (2000), 33-62. ^[12]
• "On the existence of soliton solutions to quasilinear Schrödinger equations" (with M. Poppenberg and Z. Wang), Calculus of Variations and Partial Differential Equations, 14 (2002), 329–344. ^[13]
• "The Liouville-Bratu-Gelfand problem for radial operators" (with J. Jacobsen), J. Differential Equations, 184(2002), 283–298. ^[14]
• "On principal eigenvalues for quasilinear elliptic differential operators: an Orlicz-Sobolev space setting" (with M. García-Huidobro, V. Le, R. Manásevich), Nonlinear Differential Equations and Applications, 6 (1999), 207–225. ^[15]
• "Radial solutions of quasilinear elliptic equations" (with J. Jacobsen), pp. 359–435 in Handbook on Differential Equations, Canada, Drabek, Fonda, editors. Elsevier, Amsterdam, 2004. ^[16]

References

1. Schmitt, Klaus (1978-03-27). "Boundary value problems for quasilinear second order elliptic equations". Nonlinear Analysis: Theory, Methods & Applications. 2 (3): 263–309. doi:10.1016/0362-546X(78)90019-6. ISSN   0362-546X.
2. Saupe, D.; Peitgen, H. O.; Schmitt, K. (1981-01-01). "Nonlinear elliptic boundary value problems versus their finite difference approximations: numerically irrelevant solutions". Journal für die reine und angewandte Mathematik (Crelle's Journal) (in German). 1981 (322): 74–117. doi:10.1515/crll.1981.322.74. ISSN   1435-5345. S2CID   7587627.
3. Peitgen, H.-O.; Schmitt, K. (1984). "Global analysis of two-parameter elliptic eigenvalue problems". Transactions of the American Mathematical Society. 283 (1): 57–95. doi: 10.1090/S0002-9947-1984-0735409-5 . ISSN   0002-9947.
4. Peitgen, H.-O.; Prüfer, M.; Schmitt, K. (1989), Peitgen, Heinz-Otto (ed.), "Global Aspects of the Continuous and Discrete Newton Method: A Case Study", Newton’s Method and Dynamical Systems, Dordrecht: Springer Netherlands, pp. 123–202, doi:10.1007/978-94-009-2281-5_4, ISBN   978-94-009-2281-5, S2CID   122092408 , retrieved 2022-10-02
5. Dancer, E. N.; Schmitt, Klaus (1987). "On positive solutions of semilinear elliptic equations". Proceedings of the American Mathematical Society. 101 (3): 445–452. doi: 10.1090/S0002-9939-1987-0908646-2 . ISSN   0002-9939.
6. Hutson, Vivian; Schmitt, Klaus (1992-09-01). "Permanence and the dynamics of biological systems". Mathematical Biosciences. 111 (1): 1–71. doi:10.1016/0025-5564(92)90078-B. ISSN   0025-5564. PMID   1515736.
7. Mawhin, Jean; Schmitt, Klaus (1988-08-01). "Landesman-Lazer Type Problems At An Eigenvalue Of Odd Multiplicity". Results in Mathematics. 14 (1): 138–146. doi:10.1007/BF03323221. ISSN   1420-9012. S2CID   16824406.
8. Schmitt, K.; Smith, H. L. (1978-01-01). "Positive solutions and conjugate points for systems of differential equations". Nonlinear Analysis: Theory, Methods & Applications. 2 (1): 93–105. doi:10.1016/0362-546X(78)90045-7. ISSN   0362-546X.
9. Schaaf, Renate; Schmitt, Klaus (1992-07-01). "Asymptotic behavior of positive solution branches of elliptic problems with linear part at resonance". Zeitschrift für Angewandte Mathematik und Physik. 43 (4): 645–676. Bibcode:1992ZaMP...43..645S. doi:10.1007/BF00946255. ISSN   1420-9039. S2CID   121195974.
10. Vy, Khoi Le; Schmitt, Klaus (1995). "Minimization problems for noncoercive functionals subject to constraints". Transactions of the American Mathematical Society. 347 (11): 4485–4513. doi: 10.1090/S0002-9947-1995-1316854-3 . ISSN   0002-9947. S2CID   54078118.
11. Le, Vy Khoi; Schmitt, Klaus (1997). Global Bifurcation in Variational Inequalities. Applied Mathematical Sciences. Vol. 123. New York, NY: Springer New York. doi:10.1007/978-1-4612-1820-3. ISBN   978-1-4612-7298-4.
12. Clément, Ph.; García-Huidobro, M.; Manásevich, R.; Schmitt, K. (2000-08-01). "Mountain pass type solutions for quasilinear elliptic equations". Calculus of Variations and Partial Differential Equations. 11 (1): 33–62. doi:10.1007/s005260050002. ISSN   1432-0835. S2CID   119809153.
13. Poppenberg, Markus; Schmitt, Klaus; Wang, Zhi-Qiang (2002-04-01). "On the existence of soliton solutions to quasilinear Schrödinger equations". Calculus of Variations and Partial Differential Equations. 14 (3): 329–344. doi:10.1007/s005260100105. ISSN   1432-0835. S2CID   123059914.
14. Jacobsen, Jon; Schmitt, Klaus (2002-09-01). "The Liouville–Bratu–Gelfand Problem for Radial Operators". Journal of Differential Equations. 184 (1): 283–298. Bibcode:2002JDE...184..283J. doi: 10.1006/jdeq.2001.4151 . ISSN   0022-0396.
15. García-Huidobro, M.; Le, V.K.; Manásevich, R.; Schmitt, K. (1999-05-01). "On principal eigenvalues for quasilinear elliptic differential operators: an Orlicz-Sobolev space setting". Nonlinear Differential Equations and Applications. 6 (2): 207–225. doi:10.1007/s000300050073. ISSN   1420-9004. S2CID   121929946.
16. Agarwal, R. P.; De Coster, C.; Došlý, O.; Habets, P.; Jacobsen, J.; Llibre, J.; Mawhin, J.; O'Regan, D.; Schmitt, K. (2004-01-01), Cañada, A.; Drábek, P.; Fonda, A. (eds.), List of Contributors, Handbook of Differential Equations: Ordinary Differential Equations, vol. 1, North-Holland, pp. vii, doi:10.1016/s1874-5725(00)80002-4, ISBN   9780444511287 , retrieved 2022-10-02