# Research

Positive solutions of Partial Differential Equations arising in Reaction Diffusion Systems (RD-Systems) and Population Biology. In particular, which is of the form:

\begin{align*} \Delta u+\lambda f(u,x,|\nabla u|)=0;& x\in\Omega\\ u=0; & x\in \partial\Omega. \end{align*}

## Papers

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.

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.

Existence results for classes of Laplacian systems with sign-changing weight, with R. Shivaji, Applied Mathematics Letters, Volume 20, Issue 5, May 2007, 558-562.

Positive solutions for a class of p-Laplacian systems with multiple parameters, with R. Shivaji, Journal of Mathematical Analysis and Applications. Volume 335, Issue 2, Pages 1013-1019

On positive solutions for a class of strongly coupled p-Laplacian systems, with R. Shivaji, 2006 International Conference in honor of Jacqueline Fleckinger. Electron. J. Diff. Eqns., Conference 16 (2007), pp. 29-34.

Population Models with Diffusion, Strong Allee Effect and Constant Yield Harvesting, with R. Shivaji and E Kellan Wampler, Journal of Mathematical Analysis and Applications, 352 (2009), 907-913

Positive Solutions for NxN Laplacian Systems with Combined Nonlinear Effects, with R. Shivaji and K. Brown. Journal of Differential and Integral Equations

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.

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.

Diffusive logistic equation with discontinuous constant yield harvesting in a heterogeneous environment, with David Perry, Jessica Schaefer, Brian Schilling, R. Shivaji and Matthew Williams. Electronic Journal of Qualitative Theory of Differential Equations, Spec. Ed. I, 2009 No. 2, 1-16;

Positive Solutions for $3\times3$ Elliptic Bi-variate Reaction Systems with Combined Nonlinear Effects, joint work with Shivaji, submitted.

Shifts of bacterioplankton metabolic profiles along the salinity gradient within the Caloosahatchee River Estuary, Florida, joint work with Hidetoshi Urakawa, Rheannon J. Ketover, Spencer D. Talmage, Juan C. Garcia, Ian Campbell, Michael L. Parsons and Ai Ning Loh

On positive entire large solutions for a class of elliptic system with weighted gradients, joint work with Peng Feng, in preparation.

A remark on the Reaction-Diffusion Model of Cancer Invasion, in preparation.