##
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:** Tuesdays and Thursdays 10-11 am or by appointment

#### Education

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

#### Teaching

**Fall, 2015**

- MAT 522-01 LEC (Introductory Functional Analysis), TR 11:00-12:15, Petty Building 227
- MAT 799-03 DIS (Dissertation)
- MAT 799-04 DIS (Dissertation)

**Spring, 2016**

- MAT 390-01 LEC (Ordinary Differential Equations), TR 11:00-12:15, Petty Building 227
- MAT 799-02 DTS (Dissertation)
- MAT 799-03 DTS (Dissertation)

**Fall, 2016**

- MAT 390-01 LEC (Ordinary Differential Equations), TR 11:00-12:15
- MAT 735-01 LEC (Ordinary Differntial Equations), TR 3:30-4:45

#### Research Interests

Applied Math, Mathematical Biology** Current Students: **Byungjae Son, Nalin Fonseka, Quinn Morris

#### Selected Recent Publications

- Diffusive logistic equation with constant yield harvesting and negative density dependent emigration on the boundary, Jerome Goddard II and R. Shivaji, J. Math. Anal. Appl., Vol.414, 2014, No. 2, pp. 561-573.
- 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.
- A three solution theorem for singular nonlinear elliptic boundary value problems, R. Dhanya, Eunkyung Ko, and R. Shivaji, J. Math. Anal. Appl., Vol. 424, 2015, No. 1, pp. 598-612.
- Bifurcation and multiplicity results for classes of p; q-Laplacian systems, R. Shivaji and B. Son, accepted for publication, Topological Methods in Nonlinear Analysis.
- Existence of positive radial solutions for superlinear semipositone problems on the exterior of a ball, Q. Morris, R. Dhanya, 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. To date, Shivaji has authored or coauthored one hundred and twenty six research papers, and served as thesis advisor for eleven Ph.D. graduates.