My Research Area is Applied Mathematics, especially problems arising in Elliptic Partial Differential Equations. I’m interested in positive solutions of Partial Differential Equations arising in Reaction Diffusion Systems (RD-Systems) and Population Biology.
Editor, Proceedings of the SEARCDE via Communications in Applied Analysis, 2019
Multiple positive solutions for classes of elliptic systems with combined nonlinear effects, with Mythily Ramaswamy and R. Shivaji, Journal of Differential and Integral Equations, Volume 19, Number 6 (2006), 669-680
An existence result for a semi-positone problem with a sign changing weight, with R. Shivaji, Abstract and Applied Analysis 2006 (2006), Article ID 70692.
Positive solutions for a class of p-Laplacian systems with multiple parameters, with R. Shivaji, Journal of Mathematical Analysis and Applications, 335 (2007), 1013-1019.
On positive solutions for a class of strongly coupled p-Laplacian systems, with R. Shivaji, The proceedings of the 2006 International conference in honor of Jacqueline Fleckinger, Electronic Journal of Differential Equations, Conf. 16 (2007), pp. 29-34.
Existence results for classes of Laplacian systems with sign-changing weight, with R. Shivaji, Journal of Applied Mathematics Letters, Volume 20, Issue 5, May 2007, 558-562.
Population Models with Diffusion, Strong Allee Effect and Constant Yield Harvesting, with R. Shivaji and E Kellan Wampler2, Journal of Mathematical Analysis and Applications, 352 (2009), 907-913.
Population Dynamics with Symmetric and Asymmetric Harvesting, with David Perry, Sarath Sasi, Jessica Schaefer, Brian Schilling, R. Shivaji and Matthew Williams 3, Electronic Journal of Qualitative Theory of Differential Equations, Spec. Ed. I, 2009 No. 2, 116; http://www.math.u-szeged.hu/ejqtde/
Multiple positive solutions for a class of p-q-Laplacian systems with multiple parameters and combined nonlinear effects, with R. Shivaji, Journal of Differential and Integral Equations, Vol. 22, Number 7-8 (2009), 669-678.
Positive Solutions for n×n Laplacian Systems with Combined Nonlinear Effects, with R. Shivaji and K. J. Brown, Journal of Differential and Integral Equations.
A remark on the entire explosive solutions for a class of elliptic system with gradient terms, joint work with Peng Feng, Int. Journal of Math. Analysis, Vol. 4, 2010, no. 51, 2529 – 2534.
Positive Solutions for 3 × 3 Elliptic Bi-variate Reaction Systems with Combined Non- linear Effects, joint work with Shivaji, Journal of Communications in Applied Analysis, 17 (2013), no. 1, 147-156.
Shifts of Bacterioplankton Metabolic Profiles along the Salinity Gradient in a Subtropical Estuary, joint work with Hidetoshi Urakawa, Rheannon D. J. Ketover, Spencer D. Talmage, Juan C. Garcia, Ian S. Campbell, Ai Ning Loh and Michael L. Parsons, ISRN Oceanagraphy, 2013 (2013), Article ID 410814. http://www.hindawi.com/ isrn/oceanography/2013/410814/
Positive Solutions for 3×3 Elliptic Bi-variate Infinite Semipositone Systems with Combined Nonlinear Effects, joint work with Jinglong Ye. Electronic Journal of Differential Equations, Conference 23 (2016), pp. 187-194. ISSN: 1072-6691. URL:http: //ejde.math.txstate.edu.
Existence of Multiple Positive Radial Solutions to Elliptic Equations in an Annulus, joint work with S. Padhi. Communications in Applied Analysis, 22, Vol. 4 (2018). pp. 695-710. ISSN: 1083-2564.
Positive Solutions To A Derivative Dependent P-Laplacian Equation With Riemann-Stieltjes Integral Boundary Conditions, joint work with S. Padhi and J. Graef. Annals Of Communications In Mathematics, Vol. 3 (2020). no. 1, pp. 7-25. ISSN: 2582-0818.
Existence Uniqueness and positive Solutions for a Nonlinear Fractional Differential Equation with Riemann-Liouville Derivatives, joint work with S. Padhi, J. Graef and S. Pati. Accepted.
Graduate Research Award – MSU
Junior Scholarship Award – FGCU