##
Ratnasingham Shivaji

H. Barton Excellence Professor

Department Head

**Office:** Petty 118 **Phone:** 334-5836 **Email address: **r_shivaj@uncg.edu**Personal web page:** www.uncg.edu/~r_shivaj/ **Starting year at UNCG: **2011**Office hours:** TR 2:00 p.m. - 3:00 p.m. and by appointment

#### Education

Ph.D. in Mathematics, Heriot-Watt University (1981)

#### Teaching

**Fall, 2016**

- MAT 735-01 LEC (Ordinary Differntial Equations), TR 3:30-4:45, Petty Building 223
- MAT 799-02 DTS (Dissertation)
- MAT 799-03 DTS (Dissertation)

**Spring, 2017**

- MAT 593-01 IND (Directed Study in Mathematics)
- MAT 709-01 IND (Topics in Computational Mathematics), W 3:30-4:45, Petty Building 303
- MAT 736-01 LEC (Partial Differential Equations), TR 3:30-4:45, Petty Building 313
- MAT 799-01 DTS (Dissertation)
- MAT 799-02 DTS (Dissertation)

**Summer Session 1, 2017**

- MAT 802-01 DTS (Dissertation Extension)
- MAT 802-02 DTS (Dissertation Extension)

**Fall, 2017**

- MAT 390-01 LEC (Ordinary Differential Equations), TR 11:00-12:15, Petty Building 224
- MAT 709-01 IND (Topics in Computational Mathematics), TR 3:30-4:45, Petty Building 224

#### Research Interests

Applied Math, Mathematical Biology** Current Students: **Byungjae Son, Nalin Fonseka, Mohan Mallick (IIT-India), Quinn Morris

#### Selected Recent Publications

- Uniqueness of positive radial solutions for a class of semipositone problems on the exterior of a ball, Eunkyung Ko, Mythily Ramaswamy, and R. Shivaji, J. Math. Anal. Appl., Vol. 423, 2015, No. 1, pp. 399-409.
- Existence of positive radial solutions for superlinear semipositone problems on the exterior of a ball, R. Dhanya, Q. Morris, and R. Shivaji, J. Math. Anal., Appl., Vol. 434, 2016, No. 2, pp. 1533-1548.
- Positive radial solutions to classes of singular problems on the exterior domain of a ball, Eun Kyoung Lee, R. Shivaji, and Byungjae Son, J. Math. Anal. Appl., Vol. 434, 2016, No. 2, pp. 1597-1611.
- Stability analysis for positive solutions for classes of semilinear elliptic boundary value problems with nonlinear boundary conditions, Jerome Goddard and R. Shivaji, accepted for publication, Proc. Royal Soc. Edin.
- On radial solutions for singular combined superlinear elliptic systems on annular domains, D. D. Hai and R. Shivaji, accepted for publication, J. Math. Anal. Appl.

#### Brief Bio

Ratnasingham Shivaji joined the University of North Carolina at Greensboro (UNCG) as H. Barton Excellence Professor and Head of the Department of Mathematics and Statistics in July 2011. Prior to joining UNCG, he served for twenty-six years at Mississippi State University (MSU), where he was honored as a W.L. Giles Distinguished Professor. He received his Ph.D in Mathematics from Heriot-Watt University in Edinburgh, Scotland in 1981 and his B.S (first class honors) from the University of Sri Lanka in 1977. Shivaji's area of specialization is partial differential equations, and in particular, nonlinear elliptic boundary value problems. His research work has applications in combustion theory, chemical reactor theory, and population dynamics, and has been funded by the National Science Foundation and the Simon's Foundation. Currently, he is serving as the PI on an NSF Math Ecology grant. He has authored over one hundred and thirty research papers. He is a member of the Editorial Board of several mathematics journals.To date, he has directed one postdoctoral student, fifteen Ph.D. students (11 graduates, 4 current), fourteen M.S. graduates and nineteen undergraduate research students (18 graduates, 1 current).