My research interests include differential and integral equations and
their applications, particularly in mathematical ecology.
- Integrodifference Models for Persistence in
Temporally Varying River Environments, (with Yu Jin (U
Nebraska-Lincoln) and M. Lewis (U
Alberta)), J. Math. Biol. 70 (2015), no. 3, p. 549 - 590.
- A Boundary Value Problem for
Integrodifference Population Models with Cyclic Kernels, (with
T. McAdam '13), Discrete Contin. Dyn. Syst., Series B, Vol. 19 (no
10), December 2014
- Selling Mathematics: Service & Quality, Journal of
Humanistic Mathematics, July (2013).
- R0-analysis of a spatiotemporal model for a
stream population, (with H. Mckenzie (U Alberta), Y. Jin (U
Alberta), and M. Lewis (U Alberta)), SIAM J. Appl. Dyn. Syst (2012), pp. 567-596.
- Traveling Waves and Shocks in a Viscoelastic Generalization of Burgers Equation, (with V. Camacho '07) and R. Guy (UC Davis), Siam J. Appl. Math., (2008) Vol. 68, pp. 1316-1332.
- As Flat As Possible, SIAM Review, Vol 49, no 3 (2007) pp. 491-507.
- Turing Patterns on Growing Spheres: The Exponential Case (with J. Gjorgjieva), Discrete Contin. Dyn. Syst., (2007), Series A, suppl., p. 436-445. Note: There is an error in the diffusion-driven calculation in this paper as kindly pointed out by Madzvamuse et al. See "Stability analysis of non-autonomous reaction-diffusion systems: the effects of growing domains, J. Math Biol. (2010)" for an alternate approach to determining the diffusion-driven instability condition.
- Approximations of Continuous Newton's Method: An Extension of Cayley's Problem, (with B. Tennis (HMC '06) and O. Lewis (HMC '05)), Electronic Journal of Differential Equations, 15, (2007), pp. 163-173. See also Magifractificator Home
Radial Solutions of Quasilinear Elliptic Differential Equations
(with K. Schmitt), pp. 359-436 in Handbook of Differential Equations, ed. by Canada, Drabek, Fonda; Elsevier, 2004.
A Liouville-Gelfand Equation for k-Hessian Operators,
Rocky Mountain J. Math., Vol. 34(2004), No 2, pp. 665-684.
The Liouville-Bratu-Gelfand Problem for Radial Operators (with
J. Differential Equations, Vol. 184(2002), No. 1, pp. 283-298.
Solutions of a Nonautonomous Differential Equation for a Sedimenting Sphere
(with A. Belmonte and A. Jayaraman),
Electron. J. Diff. Eqns., Vol. 2001(2001), No. 62, pp. 1-17.
- A Globalization of the Implicit Function Theorem wth Applications to Nonlinear Elliptic Equations, in Second Summer School in Nonlinear Analysis (Cuernavaca, Morelos, 2000), Amer. Math. Soc., Providence, RI, 2001, pp. 249-272.
- Global Bifurcation Problems Associated with k-Hessian Operators, Topol. Methods Nonlinear Anal., 14 (1999), pp. 81-130.
- Global Bifurcation Problems for Monge-Ampere Operators, In Nonlinear Analysis and its Applications to Differential Eqauations (Lisbon, 1998), Birkhauser, Boston, MA, 2000, pp. 299-309.