# Research: Applied Math

## Graduate Student Publications and Presentations

### Quinn Morris

**Publications**

- Q. Morris, R. Shivaji, & I. Sim. (2016). Existence of positive radial solutions for a superlinear semipositone p-Laplacian problem on the exterior of a ball. To appear in Proc. Roy. Soc. Edinburgh Sec. A.
- R. Dhanya, Q. Morris, & R. Shivaji (2016). Existence of positive radial solutions for superlinear, semipositone problems on the exterior of a ball. J. Math. Anal. Appl. 434(2016):1533-1548.
- Q. Morris & S. Robinson. (2013). A Landesman-Lazer condition for the boundary-value problem -u”=au
^{+}+bu^{–}+g(u) with periodic boundary conditions. Ninth MSU-UAB Conference on Differential Equations and Computational Simulations. Electronic Journal of Differential Equations, Conference 20(2013):103-117. - Q. Morris, R. Shivaji, & B. Son. (2016). Exact bifurcation curves for classes of positone and semipositone problems with nonlinear boundary conditions. In preparation.
- J. Goddard II, Q. Morris, C. Payne, J. Price, & R. Shivaji. (2016). Analysis of steady states for classes of reaction diffusion equations with U-shaped density dependent dispersal on the boundary. In preparation.

**Presentations**

- Analysis of steady states for classes of reaction-diffusion equations with U-shaped density dependent dispersal on the boundary. AMS Southeastern Sectional Meeting. Special Session on Nonlinear Boundary Value Problems.(Nov 2016).
- Positive, radial solutions for a superlinear semipositone
*p*-Laplacian problem on the exterior of a ball. 11th AIMS Conference on Dynamical Systems, Differential Equations, and Applications. Special Session on Advances in Theory & Application of Reaction Diffusion Models. (July 2016). - Existence of positive, radial solutions for superlinear, semipositone problems on the exterior of a ball. Joint Mathematics Meetings. Special Session on Advances in the Theory and Application of Reaction Diffusion Models. (Jan 2016).
- Existence of positive, radial solutions for superlinear, semipositone problems on the exterior of a ball. AMS Western Sectional Meeting. Special Session on Nonlinear PDE and Variational Methods.(April 2016).
- Analysis of steady states for classes of reaction-diffusion equations with U-shaped density dependent dispersal on the boundary. 2016 Southeastern Atlantic Regional Conference on Differential Equations. (Nov 2016).
- Analysis of steady states for classes of reaction-diffusion equations with U-shaped density dependent dispersal on the boundary. 2016 International Symposium on Biomathematics and Ecology Education and Research. (Oct 2016).
- Positive radial solutions for superlinear, semipositone problems on the exterior of a ball. 2015 Southeastern Atlantic Regional Conference on Differential Equations. (Oct 2016).
- Positive, radial solutions of superlinear, semipositone problems. 2015 Triangle Area Graduate Mathematics Conference. (Mar 2016).
- Positive, radial solutions of superlinear, semipositone problems. 2014 MSU Conference on Differential Equations & Computational Simulations. (Oct 2016).
- A Landesman-Lazer condition for the boundary value problem -u”=au
^{+}+bu^{–}+g(u). 2013 MAA Southeastern Sectional Meeting. (Mar 2016). - From theory to practice: boundary value problems and
*Prokelisia marginata*. Spelman College Mathematics Seminar. (Oct 2016). - Analysis of steady states for classes of reaction diffusion equations with U-shaped density dependent dispersal on the boundary. NSF REU in Mathematical Biology at UNCG Lecture Series. (Jul 2016).
- Variational Methods in Nonlinear Partial Differential Equations: A Three Part Series. UNCG Applied Math Seminar. (Mar 2016).
- Positive radial solutions for superlinear, semipositone problems. Wake Forest University Math Department Colloquium Series. (Oct 2016).

### Catherine Payne

**Publications**

- A semidiscrete approximation scheme for linear neutral delay-differential equations which preserves adjoint semigroup convergence, Richard Fabiano and Catherine Payne, accepted for publication, Proceedings of the 55th IEEE Conference on Decision and Control.
- Stability of the solution semigroup for neutral delay-differential equations, Richard Fabiano and Catherine Payne, submitted.
- Spline approximation for linear neutral systems, Richard Fabiano and Catherine Payne. In preparation.
- Analysis of steady states for classes of reaction diffusion equations with U–shaped density dependent dispersal on the boundary, Jerome Goddard II, Quinn Morris, Catherine Payne, J. Price, and R. Shivaji.In preparation.
- Fibers of continuous real-valued functions on ψ-spaces, Jerry Vaughan and Catherine Payne, Topology and its Applications, Volume 195 (2015), pp.\ 256–264.

**Presentations**

- Approximations of linear neutral delay differential equations, AMS Fall Sectional Meeting, Raleigh, NC, November 2016.
- Approximations of linear neutral delay differential equations, Southeastern-Atlantic Regional Conference on Differential Equations, Fort Myers, FL, November 2016.
- Stability conditions for linear neutral delay differential equations, Joint Mathematics Meetings, January 2016.
- Stability conditions for linear neutral delay differential equations, Southeastern-Atlantic Regional Conference on Differential Equations, Greensboro, NC, October 2015.
- Fibers of continuous real-valued functions on ψ-spaces, Spring Topology Conference, Richmond, VA, March 2014.
- Continuous functions on ψ-spaces,, AMS Fall Sectional Meeting, Greensboro, NC, November 2014

### Byungjae Son

**Publications**

- A uniqueness result for a semipositone
*p*-Laplacian problem on the exterior of a ball, R. Shivaji, Inbo Sim and Byungjae Son, Journal of Mathematical Analysis and Applications, 445 (2017), no. 1, 459-475. - Positive radial solutions to classes of singular problems on the exterior domain of a ball, Eun Kyoung Lee, R. Shivaji and Byungjae Son, Journal of Mathematical Analysis and Applications 434 (2016), no. 2, 1597-1611.
- Bifurcation and multiplicity results for classes of p, q Laplacian systems, R. Shivaji and Byungjae Son, Topological Methods in Nonlinear Analysis, 48 (2016), no. 1, 103-114.
- Uniqueness of positive solutions for a singular nonlinear eigenvalue problem when a parameter is large, Eunkyung Ko, Eun Kyoung Lee, R. Shivaji and Byungjae Son, Bulletin of the Belgian Mathematical Society. Simon Stevin 21 (2014), no. 1, 179-184.

**Presentations**

- AMS Fall Southeastern Sectional Meeting, North Carolina State University, Raleigh, NC, November 2016.
- The 11th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Hyatt Regency, Orlando, FL, July 2016.
- Spring Western Sectional Meeting, University of Nevada, Reno, NV, April 2015.
- AMS Fall Southeastern Sectional Meeting, University of North Carolina at Greensboro, Greensboro, NC, November 2014.
- The 36th Southeastern-Atlantic Regional Conference on Differential Equations, Florida Gulf Coast University, Fort Myers, FL, November 2016.
- 2016 Joint Mathematics Meetings, Washington State Convention Center, Seattle, WA, January 2016.
- The 11th Annual UNCG Regional Mathematics and Statistics Conference, University of North Carolina at Greensboro, Greensboro, NC, November 2015.
- The 35th Southeastern-Atlantic Regional Conference on Differential Equations, University of North Carolina at Greensboro, Greensboro, NC, October 2015.
- Triangle Area Graduate Mathematics Conference, North Carolina State University, Raleigh, NC, March 2015.
- 10th Mississippi State Conference on Differential Equations and Computational Simulations, Mississippi State University, Starkville, MS, October 2014.
- The 9th Annual UNCG Regional Mathematics and Statistics Conference, University of North Carolina at Greensboro, Greensboro, NC, 2013.
- The 33rd Southeastern-Atlantic Regional Conference Differential Equations, University of Tennessee, Knoxville, TN, 2013.