Research:

Currently, Ananta Acharya continues his research in mathematical ecology and mathematical biology while serving as an Assistant Professor of Mathematics at Eastern New Mexico University. Prior to this appointment, Dr. Acharya joined Utah State University in August 2023 as a temporary Assistant Professor of Mathematics for postdoctoral research. During his time at USU, he was actively involved in the Partial Differential Equations research group led by Zhi-Qi Wang, the MathBio research group led by Jim Powell, and the Applied Mathematics Education research group led by Brynja Kohler.

Dr. Acharya’s Ph.D. advisor was Prof. Ratnasingham Shivaji at the University of North Carolina at Greensboro. His doctoral research focused on differential equations, particularly nonlinear elliptic boundary value problems, and mathematical ecology. Specifically, his work examined steady-state reaction–diffusion equations modeling population dynamics, including density-dependent dispersal on the boundary and the effects of exterior matrix hostility. In particular, he studies positive solutions to classes of steady-state reaction–diffusion equations in which parameters influence both the equations and the boundary conditions.

To date, Dr. Acharya has collaborated with more than eight researchers, including an ecologist and two undergraduate students. His research has resulted in publications in several peer-reviewed 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 Dr. Acharya has worked on were supported by his advisor’s NSF grant. He is currently engaged in multiple ongoing research projects. A list of his published articles can be found at the following links:

• Σ-Shaped bifurcation curves influenced by nonlinear boundary conditions for classes of reaction diffustion systems 

• A Σ-shaped bifurcation curves for a class of reaction diffusion equations and an application to an ecological model. 

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

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

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

• Sigma-shaped bifurcation curves for classes of elliptic systems

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

• Sigma Shaped Bifurcation Curves

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