Jeffrey Lyons, Ph.D.

Associate Professor
Department of Mathematics
(954) 262-7931
jlyons@nova.edu

     Education:      Research Interest(s):     Courses Taught: 

My research is primarily in the field of boundary value problems for differential, difference, and dynamic equations. Current research includes: 

  • Fixed point theory 
  • Boundary data smoothness 
  • Green’s functions
1. J. Champion, J.A. Franco, J. W. Lyons, “Arithmagons and Geometrically Invariant Multiplicative Integer Partitions,”Acta Math. Univ. Comenianae, 85 (2016), 87-95. 
2. J.W. Lyons, “An Application of an Avery Type Fixed Point Theorem to a Second Order Antiperiodic Boundary Value Problem,” AIMS Ser. Differ. Equ. Dyn. Syst., AIMS Proceedings (2015), 775-782. 
3. P. Eloe, J.W. Lyons, J.T. Neugebauer, “An Ordering on Green’s Functions for a Family of Two-Point Boundary Value Problems for Fractional Differential Equations,”Commun. Appl. Anal., 19 (2015), 453-462. 
4. J.W. Lyons, J.T. Neugebauer, “Existence of an Antisymmetric Solution of a Boundary Value Problem with Antiperiodic Boundary Conditions,” Electron. J. Qual. Theory Differ. Equ., 2015, no. 72, 1-11. 
5. J.W. Lyons, J.K. Miller, “The Derivative of a Solution to a Second Order Parameter Dependent Boundary Value Problem with a Nonlocal Integral Boundary Condition,” Journal of Mathematics and Statistical Science, 1 (2015), no. 2, 43-50. 
6. J.W. Lyons, J.T. Neugebauer, “A Difference Equation with Anti-Periodic Boundary Conditions,” Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 22 (2015), no. 1, 47-60. 
7. A.F. Janson, B.T. Juman, J.W. Lyons, “The Connection between Variational Equations and Solutions of Second Order Nonlocal Integral Boundary Value Problems,” Dyn. Syst. Appl., 23 (2014), no. 2-3, 493-503. 
8. J.W. Lyons, “On Differentiation of Solutions of Boundary Value Problems for Second Order Dynamic Equations on a Time Scale,” Commun. Appl. Anal., 18 (2014), 215-224. 
9. J.W. Lyons, J.T. Neugebauer, “Existence of a Positive Solution for a Right Focal Dynamic Boundary Value Problem,” Nonlinear Dyn. Syst. Theory, 14 (2014), no. 1, 76-83. 
10. J.W. Lyons, “Disconjugacy, Differences, and Differentiation for Solutions of Nonlocal Boundary Value Problems for nth Order Difference Equations,” J. Difference Equ. Appl., 20 (2014), no. 2, 296-311. 
11. J.W. Lyons, “Differentiation of Solutions of Nonlocal Boundary Value Problems with Respect to Boundary Data,” Electron. J. Qual. Theory Differ. Equ., 2011, no. 51, 1-11. 
12. D.R. Anderson, R.I. Avery, J. Henderson, X. Liu, J.W. Lyons, “Existence of a Positive Solution for a Right Focal Discrete Boundary Value Problem,” J. Difference Equ. Appl. 17 (2011), no. 11, 1635-1642. 
13. J. Henderson, X. Liu, J.W. Lyons, J.T. Neugebauer, “Right Focal Boundary Value Problems for Difference Equations,” Opuscula Math. 30 (2010), no. 4, 447-456. 
14. J. Henderson, J.W. Lyons, “Characterization of Partial Derivatives with Respect to Boundary Conditions for Solutions of Nonlocal Boundary Value Problems for nth Order Differential Equations,” Int. J. Pure Appl. Math. 56 (2009), no. 2, 235-257. 
15. B. Hopkins, E. Kim, J.W. Lyons, K. Speer, “Boundary Data Smoothness for Solutions of Nonlocal Boundary Value Problems for Second Order Difference Equations,” Comm. Appl. Nonlinear Anal. 16 (2009), no. 2, 1-12.
1. The Derivative of a Solution to a Second Order Parameter Dependent Boundary Value Problem with a Nonlocal Integral Boundary Condition, The 35th Southeastern Atlantic Regional Conference on Differential Equations (SEARCDE), University of North Carolina – Greensboro, Greensboro, NC, October 10-11, 2015. 
2. An Ordering on Green’s Functions for a Family of Two-point Boundary Value Problems for Fractional Differential Equations, The 10th Mississippi State Conference on Differential Equations and Computational Simulation (DECS), Mississippi State University, Starkville, MS, October 23-25, 2014. 
3. An Application of an Avery Type Fixed Point Theorem to a Second Order Antiperiodic Boundary Value Problem, Special Session on Applications of Topological and Variational Methods to Boundary Value Problems, 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Madrid, Spain, July 7-11, 2014. 
4. Characterizing Derivatives of Solutions to Nonlocal Boundary Value Problems with Parameter, Special Session on Lie Symmetries, Conservation Laws and Other Approaches in Solving Nonlinear Differential Equations, 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Madrid, Spain, July 7-11, 2014. 
5. Existence of Antisymmetric Solutions for Second Order Difference Equations with Antiperiodic Boundary Conditions, Special Session on Difference Equations and Applications, AMS and MAA Joint Mathematics Meeting, Baltimore, MD, January 15-18, 2014. 
6. Derivatives of the Solution to a Dynamic Boundary Value Problem on a General Time Scale, The 34th Southeastern Atlantic Regional Conference on Differential Equations (SEARCDE), University of Memphis, Memphis, TN, October 11-12, 2014. 
7. Existence of Symmetric and Anti-symmetric Solutions for Second Order Boundary Value Problems with Periodic and Anti-periodic Boundary Conditions, Special Session on Fixed Point Theorems and Applications to Integral, Difference, and Differential Equations, Fall Southeastern Sectional Meeting of the American Mathematical Society, University of Louisville, Louisville, KY, October 5-6, 2013. 
8. Variational Equations and Solutions of Second Order BVPs with Integral Boundary Conditions, The 33rd Southeastern Atlantic Regional Conference on Differential Equations (SEARCDE), University of Tennessee, Knoxville, Knoxville, TN, September 21-22, 2013. 
9. Disconjugacy and Differentiation for Solutions of Boundary Value Problems for Second-Order Dynamic Equations on a Time Scale, Mathematics Colloquium Series, Nova Southeastern University, Ft Lauderdale, FL, April 10, 2013. 
10. Characterizing Boundary Data Smoothness for Solutions of Difference, Differential, and 
Dynamic Boundary Value Problems, Department of Mathematics Colloquium, University of Dayton, Dayton, OH, March 19, 2013. 
11. Characterizing Boundary Data Smoothness for Solutions of Difference, Differential, and Dynamic Boundary Value Problems, Mathematics Colloquium, Eastern Kentucky University, Richmond, KY, March 18, 2013. 
12. Generalizing the Discrete and Continuous Domains of Boundary Data Smoothness for Solutions of Second Order Boundary Value Problems, New Trends in Differential and Difference Equations Conference, The University of Tennessee at Chattanooga, Chattanooga, TN, March 15-16, 2013. 
13. Existence of a Positive Solution for a Right Focal Dynamic Boundary Value Problem, International Conference on the Theory, Methods, and Applications of Nonlinear Equations, Texas A&M University – Kingsville, Kingsville, TX, December 17-21, 2012. 
14. Existence of a Positive Solution for a Right Focal Dynamic Boundary Value Problem, The 32nd Southeastern Atlantic Regional Conference on Differential Equations (SEARCDE), Wake Forest University, Winston-Salem, NC, October 19-20, 2012. 
15. Getting from Good to Great: What do the Statistics Show?, NCCEP/GEAR UP Annual Conference, San Francisco, CA, July 17-20, 2011, Co-Presenter with F. M. Abudiab, M. A. Abudiab, P. Tintera, M. C. Venzon.