Research:

I joined Utah State University in August 2023 as a temporary Assistant Professor of Mathematics. I have been involved in Mathbio research group of Jim Powell and Applied Math Education research group of Brynja Kohler at USU.

My Ph.D. advisor is Prof. Ratnasingham Shivaji at University of North Carolina, Greensboro. My PhD research is focused on Differential Equations (Nonlinear Elliptic Boundary Value Problems) and Mathematical Ecology (Steady State Reaction-Diffusion Equations modeling population dynamics, including the density-dependent dispersal on the boundary and effects of exterior matrix hostility). In particular, I study positive solutions to classes of steady-state reaction-diffusion equations where a parameter influences the equation as well as the boundary conditions. To date, I  have collaborated with over 8 researchers including an ecologist and two undergraduate students. My research work has resulted in articles published in several journals including Advances in Nonlinear Analysis, Nonlinear Analysis: Real World Applications, Boundary Value Problems, Electronic Journal of Differential Equations, Discrete and Continuous Dynamical Systems - Series S, Electronic Journal of Qualitative Theory of Differential Equations, and  Discrete and Continuous Dynamical Systems - Series B.

Many of the ecological research projects I worked on have been supported by my advisor's NSF grant. Currently I am working in multiple research projects. So far published articles can be found in the following links:

• Analysis of reaction–diffusion systems where a parameter influences both the reaction terms as well as the boundary 

• Sigma Shaped Bifurcation Curves 

• Existence and Multiplicity Results for p-q-Laplacian boundary value problems  

• Sigma-shaped bifurcation curves for classes of elliptic systems 

• The diffusive Lotka-Volterra competition model in fragmented patches I: Coexistence 

• An exact bifurcation diagram for ap–q Laplacian boundary value problem 

• On the effects of density-dependent emigration on ecological models with logistic and Weak Allee type growth terms