Siegfried Carl

Professor of Mathematics

Professor of Mathematics

**Contact**Phone +49 345 5524639 Fax +49 345 5527003 Email siegfried.carl@mathematik.uni-halle.de

**Postal Address**Prof. Dr. Siegfried Carl Martin-Luther-Universität Halle-Wittenberg Institut für Mathematik 06099 Halle, Germany

**Research Interests**- Nonlinear Analysis - Nonsmooth Variational Problems

(Variational- and Hemivariational Inequalities) - Nonlinear Elliptic and Parabolic Differential Equations and Inclusions - Comparison Principles - Multiple Solutions in Nonlinear Elliptic Problems - Nonlinear Eigenvalue Problems

Siegfried Carl - Professor of Mathematics

Curriculum Vitae

**Education**

- 1975 Master in Mathematics (Diploma in Mathematics), University of Halle, Germany
- 1984 Ph.D. in Mathematics (Dr.rer.nat.), University of Halle, Germany
- 1990 postdoctoral qualification - Dr.rer.nat.habil. (Habilitation), Department of Mathematics and Computer Science, Institute of Technology (Technische Hochschule), Merseburg, Germany

**Employment**

- 1975-1981 Researcher, Academy of Science Institute of Solid State Physics and Electron Microscopy, Halle, Germany
- 1981-1984 Ph.D.-Research Fellow, Department of Mathematics, University of Halle, Germany
- 1984-1993 Assistant and Senior Assistant, Department of Mathematics and Computer Science, Institute of Technology, Merseburg, Germany
- 1993-1995 Privatdozent, Department of Mathematics and Computer Science, University of Halle, Germany
- since 1995 Professor of Mathematics, Institute of Mathematics, University of Halle, Germany

**Visiting Positions (A selection of stays of one month and longer)**

- 1990 (1 month) Department of Mathematics, University of Oulu, Finland
- 1994 (2 months) Department of Applied Mathematics, Florida Institute of Technology, Melbourne, FL, USA
- 1994, LEOPOLDINA-RESEARCH GRANT AWARD from GERMAN ACADEMY OF SCIENCES LEOPOLDINA (including a Leopoldina Scholarship for a 6-months research stay abroad)
- 1995 (6 months) Department of Mathematics, North Carolina State University, Raleigh, USA
- 1996 (1 month) Department of Mathematics, University of Oulu, Finland
- 1997 (1 month) Department of Mathematics, University of Oulu, Finland
- 1998 (5 weeks) Department of Mathematics, University of Oulu, Finland
- 2000 (1 month) Department of Mathematical Sciences, University of Delaware, USA and Department of Applied Mathematics, Florida Institute of Technology, Melbourne, FL, USA
- 2001-2002 (1 academic year) Visiting Professor at the Department of Applied Mathematics, Florida Institute of Technology, Melbourne, FL, USA
- 2005 (1 month) Visiting Professor at the Department of Mathematics, University of Perpignan, France
- 2008 (1 month) Visiting Professor at the Department of Mathematics, University of Perpignan, France

Siegfried Carl - Professor of Mathematics

Publications

**Monographs**

- Siegfried Carl and Seppo Heikkilä, Fixed Point Theory in Ordered Sets and Applications, Springer, New York, 2011.
- Siegfried Carl, Vy Khoi Le, and Dumitru Motreanu, Nonsmooth Variational Problems and Their Inequalities, Springer Monographs in Mathematics, Springer, New York, 2007.
- S. Carl and S. Heikkilä, Nonlinear Differential Equations In Ordered Spaces, Chapman & Hall/CRC, London, 2000.

**Recent Research Articles**(a list of all publications as pdf-file can be downloaded here)

- Carl, S., N-Laplacian elliptic equations in exterior domains via Kelvin transform, Pure and Applied Functional Analysis (in: Special Issue of the journal Pure and Applied Functional Analysis dedicated to Professor H. Brezis) to appear
- Carl, S., and Vy K. Le, Extremal solutions of multi-valued variational inequalities in plane exterior domains, J. Differential Equations (2019), https://doi.org/10.1016/j.jde.2019.05.020
- Carl, S., Costa, David G., Fotouhi, M., and Tehrani, H.,
Invariance of critical points under Kelvin transform and multiple solutions in exterior domains of R^2,
Calc. Var. Partial Differential Equations
**58**(2019), no. 2, Art. 65, 24 pp. - Carl, S., Costa, David G., and Tehrani, H.,
Extremal solutions of logistic-type equations
in exterior domain in R^2,
Nonlinear Anal.
**176**(2018), 272-287. - Carl, S., Tietz, Ch.,
Quasilinear elliptic equations with measures and multi-valued lower order terms,
Discrete Contin. Dyn. Syst. Ser. S
**11**(2018), no. 2, 193-212. - Carl, S.,
Decay estimates for Wolff potentials in R^N and gradient-dependent quasilinear elliptic equations,
J. Differential Equations
**265**(2018), no. 8, 3685-3708. - Carl, S., and Motreanu, D.,
Extremal solutions for quasilinear parabolic systems in trapping regions,
Pure and Applied Functional Analysis
**3**(2018), no. 1, 57-74. - Carl, S., Costa, David G., and Tehrani, H.,
D^{1,2}(R^N) versus C(R^N) local minimizer on manifolds and multiple solutions for zero-mass equations in R^N,
Advances in Calculus of Variations
**11**(2018), no. 3, 257-272. - Carl, S.,
Extremal solutions of p-Laplacian problems in D^{1,p}(R^N) via Wolff potential estimates,
J. Differential Equations
**263**(2017), 3370-3395. - Carl, S., and Motreanu, D.,
Extremal solutions for nonvariational quasilinear elliptic systems via expanding trapping regions,
Monatsh Math
**182**(2017), no. 4, 801-821. - Carl, S., Costa, David G., and Tehrani, H.,
D^{1,2}(R^N) versus C(R^N) local minimizer and a Hopf-type maximum principle,
J. Differential Equations
**261**(2016), 2006-2025. - Carl, S., Costa, David G., and Tehrani, H.,
Extremal and sign-changing solutions of supercritical logistic-type equations in R^N,
Calc. Var. Partial Differential Equations
**54**(2015), no. 4, 4143-4164. - Carl, S.,
Barrier solutions of elliptic variational inequalities,
Nonlinear Anal. Real World Appl.
**26**(2015), 75-92. - Carl, S., and Motreanu, D.,
Multiple solutions for elliptic systems via trapping regions and related nonsmooth potentials,
Appl. Anal.
**94**(2015), no. 8, 1594-1613. - Carl, S., and D'Ambrosio, L.,
Foreword [Nonlinear partial differential equations, in honor of Enzo Mitidieri on his 60th birthday],
Nonlinear Anal.
**121**(2015), 1-2. - Carl, S., and Vy K. Le,
Elliptic inequalities with multi-valued operators: existence, comparison and related variational-hemivariational type inequalities, Nonlinear Anal.
**121**(2015), 130-152. - Carl, S., and Le, V. K.,
Multi-Valued Parabolic Variational Inequalities and Related Variational-Hemivariational Inequalities,
Advanced Nonlinear Studies
**14**(2014), 603-631. - Carl, S., and Le, V. K.,
Quasilinear Parabolic Variational Inequalities with Multi-Valued Lower Order Terms,
Z. Angew. Math. Phys.
**65**(2014), 845-864 - Carl, S.,
Existence and Extremal Solutions of Parabolic Variational-Hemivariational Inequalities,
Monatsh. Math.
**172**(2013), 29-54. - Candito, P., Carl, S., and Livrea, R.,
Variational versus pseudomonotone operator approach in parameter-dependent nonlinear elliptic problems, Dynam. Systems Appl.
**22**(2013), 397-410. - Carl, S.,
Signorini type variational inequality with state-dependent discontinuous multivalued boundary operators,
Nonlinear Anal.
**92**(2013), 138-152. - Carl, S.,
Elliptic variational inequalities with discontinuous multi-valued lower order terms, Adv. Nonlinear Stud.
**13**(2013), 55-78.

Siegfried Carl - Professor of Mathematics

Editorial Work

**Editorial Board Member of the following international mathematical journals:**

- Associate Editor: Journal of Inequalities and Applications (January 2003 - December 2011)
- Associate Editor: Nonlinear Analysis (2004 - 2009)
- Associate Editor: Nonlinear Analysis: Real World Applications (January 2009 - March 2012)
- Associate Editor: Applicable Analysis (since 2001)
- Editor-in-Chief: Nonlinear Analysis (2009 - 2019)
- Honorary Editor: Nonlinear Analysis (since 2019)

Siegfried Carl - Professor of Mathematics

Teaching

**The following list provides a selection of courses taught in recent years:**

- Basic courses in Analysis:
- Real Analysis in one and higher dimensions
- Ordinary Differential Equations
- Function Theory of One Complex Variable
- Measure Theory

- Introduction to Linear Functional Analysis
- Nonlinear Analysis:
- Monotone and Pseudomonotone Operators
- Variational Inequalities
- Variational Methods

- Partial Differential Equations
- Functional Analysis and its Applications to Partial Differential Equations
- Differential Inequalities: Maximum and Comparison Principles

Siegfried Carl - Professor of Mathematics

Projects

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