# People

## Ratnasingham Shivaji

### Professor

H. Barton Excellence Professor

Fellow of the American Mathematical Society

**Office:** Petty 148**Email: **r_shivaj@uncg.edu**Personal Website: **http://www.uncg.edu/~r_shivaj/**Starting year at UNCG:** 2011

### Education

**Degree(s): **Ph.D. in Mathematics, Heriot-Watt University (1981)

### Teaching

**Fall 2019**

- MAT-735 LEC (Ordinary Differential Equations), TR 11:00-12:15, Graham Building 303
- MAT-709 LEC (Topics in Computational Mathematics), TR 3:30-4:45, Petty Science Building 107
- MAT-488 IND (Directed Study in Mathematics)
- MAT-790 IND (Directed Doctoral Research)
- MAT-799 DTS (Dissertation)

### Research

**Member of the Research Group(s):** Applied Math, Mathematical Biology**Current Students:** Amila Muthunayake (Ph.D.), Nalin Fonseka (Ph.D.), Ananta Acharya (Ph.D.)**Former Students:** Mohan Mallick (Ph.D. 2019), Quinn Morris (Ph.D. 2017), Byungjae Son (Ph.D. 2017), Dagny Butler (Ph.D. 2014), Lakshmi Sankar (Ph.D. 2013), Eunkyung Ko (Ph.D. 2012), Sarath Sasi (Ph.D. 2012), Jerome Goddard II (Ph.D. 2011), Jinglong Ye (Ph.D. 2009), Jaffar Ali (Ph.D. 2008), Scott Caldwell (Ph.D. 2003), Shobha Oruganti (Ph.D. 2002), Anuradha Vishwanathan (Ph.D. 1994), Eun Kyoung Lee (Post. Doct. 2007 - 2009)

**Research Interests:** Study of non-negative solutions to partial differential equations, arising in the modeling of natural phenomena that is dominated by reaction and diffusion. Recent results focus on singular problems, problems with nonlinear diffusion and effects of nonlinear boundary conditions.

### Selected Publications

- Positive solutions for a class of non-cooperative
*pq*-Laplacian systems with singularities, K.D. Chu, D.D. Hai, R. Shivaji, Applied Math Letters (accepted for publication 2018). - A diffusive logistic equation with U-shaped density dependent dispersal on the boundary, J. Goddard, Q. Morris, C. Payne, and R. Shivaji, Topological Methods in Nonlinear Analysis (accepted for publication 2018).
- Uniqueness of positive radial solutions for infinite semipositone
*p*-Laplacian problems in exterior domains, K. D. Chu, D. D. Hai, R. Shivaji, J. Math Anal. Appl. (accepted for publication 2018). - Analysis of positive radial solutions for a class of semipositone
*p*-Laplacian problems with nonlinear boundary conditions, E. Lee, R. Shivaji, I. Sim, and B. Son, Commun. Pure Appl. Anal. (accepted for publicatin 2018). - Existence and multiplicity of positive radial solutions for singular superlinear elliptic systems in the exterior of a ball, D. D. Hai and R. Shivaji, J. Differential Equations (accepted for publications 2018).

### Brief Biography

Ratnasingham Shivaji joined the University of North Carolina at Greensboro (UNCG) as Head in July 2011. Since January 2012, he is also serving as H. Barton Excellence Professor. 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. He is a Fellow of the American Mathematical Society. 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. To date, he has authored one hundred fifty one research papers. He is a member of the Editorial Board of several mathematics journals. To date, he has directed one postdoctoral student, seventeen Ph.D. students (14 graduates, 3 current), fifteen M.S. graduates, and twenty-eight undergraduate research students (3 current).