Ratnasingham Shivaji

Ratnasingham Shivaji

H. Barton Excellence Professor
Fellow of the American Mathematical Society

Office: Petty 148
Personal Website:
Starting year at UNCG: 2011
Office Hours: Virtual: T,Th 12:15pm-1pm & T,Th 4:45pm-5:30pm and by appointment


Degree(s): Ph.D. in Mathematics, Heriot-Watt University (1981), B.Sc (First Class Honors) (Special Degree in Mathematics), University of Sri Lanka, Peradeniya (1977)


Fall 2020
  • MAT-390 LEC (Ordinary Differential Equatns), TR 11:00-12:15
  • MAT-735 LEC (Ordinary Differntial Equations), TR 3:30-4:45
  • MAT-701 SEM (Sel Topics Computational Math), F 1:00-4:00
  • MAT-799 DTS (Dissertation)


Member of the Research Group(s): Applied Math, Mathematical Biology
Current Students: Amila Muthunayake (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 (Postdoc. 2007 - 2009)

Research Interests: Study of non-negative solutions to steady state reaction diffusion equations arising in the modeling of natural phenomena including ecology and combustion theory. Recent results focus on singular problems, nonlinear diffusion, and nonlinear boundary conditions.

Selected Publications

  • Uniqueness of positive radial solutions for infinite semipositone p-Laplacian problems in exterior domains, K.D. Chu, D.D. Hai, and R. Shivaji, J. Math. Anal. Appl. 472 (2019), no. 1, 510–525
  • 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 266 (2019), no. 4, 2232–2243
  • S-shaped bifurcation diagrams in exterior domains, M. Chhetri, P. Drabek, and R. Shivaji, Positivity (accepted for publication 2019)
  • Effects of patch-matrix composition and individual movement response on population persistence at the patch-level, J. Cronin, J. Goddard, and R. Shivaji, Bull. Math. Biol. (accepted
    for publication 2019)
  • Uniqueness of positive radial solutions for a class of infinite semipositone p-Laplacian problems in a ball, K. D. Chu, D. D. Hai, and R. Shivaji, Proceedings of the AMS (accepted for publication 2019)

Brief Biography

Ratnasingham Shivaji joined the University of North Carolina at Greensboro (UNCG) as Head in July 2011 and served in this position until July 2019. 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 five 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 (fourteen graduates, 3 current), fifteen M.S. graduates, and thirty undergraduate research students (twenty eight past, 2 current).