Published Research by Mathematics Faculty

The Department of Mathematics prides itself on a tradition of active and productive research. Recent published research by UTC Department of Mathematics faculty members of the department are listed below.


Published in 2016: 

  1. J.R. Graef, L. Kong, and B. Yang, Positive solutions for a fractional boundary value problem, Applied Mathematics Lecers 56 (2016), 49–55.

  2. J.R. Graef, L. Kong, Y. Tian, and M. Wang, Three solutions for second-order impulsive differential inclusions with Sturm-Liouville boundary conditions via nonsmooth critical point theory, Topological Methods in Nonlinear Analysis 47 (2016), 1–18.

  3. J.R. Graef, A. Baliki and M. Benchohra, Global existence and stability for second order functional evolution equations with infinite delay, Electronic Journal of Qualitative Theory of Differential Equations (2016), No. 23, 1–10.

  4. B.C. Dhage, S.B. Dhage, and J.R. GraefDhage iteration method for initial value problems for nonlinear first order hybrid integro-differential equations, Journal of Fixed Point Theory and Applications 18 (2016), 309–326.

  5. J.R. Graef, C. Tunc and S. Sevgin, Behavior of solutions of nonlinear functional Volterra integro-differential equations with multiple delays, Dynamic Systems and Applications 25 (2016), 39–46.

  6. J.R. Graef, S. Heidarkhani, and L. KongMultiple solutions for systems of Sturm-Liouville boundary value problems, Mediterranean Journal of Mathematics 13 (2016), 1625–1640.

  7. B.C. Dhage, S.B. Dhage, and J.R. GraefLocal attractivity and stability analysis of a nonlinear quadratic fractional integral equation, Applicable Analysis 95 (2016), 1989–2003.

  8. S. R. Grace, J.R. Graef, and E. Tunc, Oscillatory behavior of a third-order neutral dynamic equation with distributed delays,
    Proceedings of the Tenth Colloquium on the Qualitative Theory of Differential Equations, Electronic Journal of Qualitative Theory of Differential Equations, 2016, No. 14, 1–14

  9. J.M. Davis, P.W. Eloe, J.R. Graef, and J. Henderson, Positive solutions for a singular fourth order nonlocal boundary value problem, International Journal of Pure and Applied Mathematics 109 (2016), 67–84.

  10. J.R. Graef, S. Heidarkhani, and L. Kong, Multiple periodic solutions for perturbed second-order impulsive Hamiltonian systems, International Journal of Pure and Applied Mathematics 109 (2016), 85–104.
  11. S. R. Grace, J.R. Graef, and E. Tunc, Asymptotic behavior of solutions of forced fractional differential equations, Electronic Journal of Qualitative Theory of Differential Equations (2016), No. 71, 1–10 (Special issue dedicated to Tibor Krisztin on the occasion of his sixtieth birthday).

  12. F. Domingo, E. Dale, C. Gao, A single-center retrospective review of postoperative infectious complications in the surgical management of mandibular fractures: Postoperative antibiotics add no benefit, J. Trauma Acute Care Surg. (2016), 81(6), 1109–1114.
  13. L. Zhu, D. Finkelstein, C. Gao, L. Shi, Y. Wang, D. Lopez-Terrada, K. Wang, S. Utley, S. Pounds, G. Neale, D. Ellison, A. Onar-Thomas, R.J. Gilbertson, Multi-organ mapping of cancer risk, Cell 166 (2016), Issue 5, 1132–1146.
  14. Y. Liang, D. Wu, Y. Li, C. Gao, J. Ma, ad W. Wu, Big data-enabled multiscale serviceable analysis about aging bridges, J. of Digitial Comm. and Networds 62 (2016), Issue 3, 97–107.
  15. C. Murphy, B. Foster, and C. Gao, Temporal dynamics in rhizosphere bacterial communities of three perennial grassland species, Agronomy (2016), 6(1), Issue 17, 117.
  16. B. Shamsaei and C. Gao, Comparison of some machine learning and statistical algorithms for classification and prediction of human cancer type, 2016 IEEE-EMBS International Conference on Biomedical and Health Informatics, Proceedings of IEEE Engineering in Medicine and Biology Society, 296–299.
  17. L. Kong, Homoclinic solutions for a higher order difference equation with p-Laplacian, Indag. Math. 27 (2016), 124–146.
  18. L. Kong, Multiple solutions for fourth order elliptic problems with p(x)-biharmonic operators, Opuscula Math. 36 (2016), 252–264.
  19. L. Kong and Qingkai Kong, Positive solutions of a singular fractional boundary value problem, Enlightenment of Pure and Applied Mathematics 2 (2016), 143–152. 
  20. J.R. Graef and Lingju Kong, Multiple Solutions of Boundary Value Problems, A Variational Approach, Trends in Abstract and Applied Analysis, Volume 1, World Scientific Publishing Company, New Jersey, 2016.
  21. L. Kong, Positive radial solutions for quasilinear biharmonic equations,Comput. Math. Appl. 72 (2016), 2878–2886.
  22. J.R. Graef, L. Kong, and Xueyan Liu, Existence of positive solutions to a discrete fourth order periodic boundary value problem, J. Difference Equ. Appl. 22 (2016), 1167–1183.
  23. J.R. Graef, L. Kong, Q. Kong, and M. Wang, On a fractional boundary value problem with a perturbation term, J. Appl. Anal. Comput. 7 (2017), 57–66.
  24. F. Gesztesy, S. Hofmann, and R. Nichols, On stability of square root domains for non-self-adjoint operators under additive perturbations, Mathematika 62 (2016), 111–182.

  25.  J. Behrndt, F. Gesztesy, H. Holden, and R. Nichols, Dirichlet-to-Neumann maps, abstract Weyl–Titchmarsh M-functions, and a generalized index of unbounded meromorphic operator-valued functions, J. Differential Equations 261 (2016), 3551–3587.
  26. X. Wang and J. Wang, Disease dynamics in a coupled cholera model linking within-host and between-host interactions, Journal of Biological Dynamics, 2016. DOI: 10.1080/17513758.2016.1231850.
  27. A. Timalsina, G. Hou, and J. Wang, Computing fluid-structure interaction by the partitioned approach with direct forcing, Communications in Computational Physics, 2016. DOI:
  28. T. Huynh, G. Hou and J. Wang, Communicating wave energy: An active learning experience for students, American Journal of Engineering Education, vol. 7, 37–46, 2016. 
  29. X. Wang, D. Posny, and J. Wang, A reaction-convection-diffusion model for cholera spatial dynamics, Discrete and Continuous Dynamical Systems – Series B, vol. 21(8), 1–25, 2016.
  30. S. Mushayabasa, D. Posny, and J. Wang, Modeling the intrinsic dynamics of foot-and-mouth disease, Mathematical Biosciences and Engineering, vol. 13, 425–442, 2016.
  31. D. Posny, C. Modnak, and J. Wang, A multigroup model for cholera dynamics and control, International Journal of Biomathematics, vol. 9(1), 1650001, 2016.
  32. A. Ledoan, Explicit formulas for the distribution of complex zeros of a family of random sums, J. Math. Anal. Appl. 444 (2016), Issue 2, 1304–1320.