Research output per year
Research output per year
Personal profile
Research interests
My current research interests are in nonlinear differential equations. Particular areas include:
global bifurcation theory
boundary value problems with jumping nonlinearities
multi-point boundary value problems.
Biography
I received my in Ph.D. from Dundee University in 1982, in which I worked on linear and nonlinear multiparameter spectral theory. Between 1983 and 1990 I was a Research Fellow in Dundee, York and Southampton Universities, working variously on electromagnetic scattering, metric number theory and nonlinear dynamical systems.
In 1990 I joined Heriot-Watt University as a lecturer in the Mathematics Department. I became a reader in 1996, and then a professor in 2009.
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Linearized stability implies dynamic stability for equilibria of 1-dimensional, p-Laplacian boundary value problems
Rynne, B. P., Jun 2020, In: Proceedings of the Royal Society of Edinburgh, Section A: Mathematics. 150, 3, p. 1313-1338 26 p.Research output: Contribution to journal › Article › peer-review
Open AccessFile1 Citation (Scopus)89 Downloads (Pure) -
Stability of solutions of a 1-dimensional, p-Laplacian problem and the shape of the bifurcation curve
Rynne, B. P., Jul 2020, In: Nonlinear Analysis: Theory, Methods and Applications. 196, 111757.Research output: Contribution to journal › Article › peer-review
Open AccessFile49 Downloads (Pure) -
Exact multiplicity and stability of solutions of a 1-dimensional, p-Laplacian problem with positive convex nonlinearity
Rynne, B. P., Jun 2019, In: Nonlinear Analysis: Theory, Methods and Applications. 183, p. 271-283 13 p.Research output: Contribution to journal › Article › peer-review
Open AccessFile5 Citations (Scopus)48 Downloads (Pure) -
Global asymptotic stability of bifurcating, positive equilibria of p-Laplacian boundary value problems with p-concave nonlinearities
Rynne, B. P., 5 Feb 2019, In: Journal of Differential Equations. 266, 4, p. 2244-2258 15 p.Research output: Contribution to journal › Article › peer-review
Open AccessFile2 Citations (Scopus)42 Downloads (Pure) -
Linearized stability implies asymptotic stability for radially symmetric equilibria of p-Laplacian boundary value problems in the unit ball in ℝN
Rynne, B. P., 29 Jul 2019, In: Electronic Journal of Differential Equations. 2019, 94, p. 1-17 17 p.Research output: Contribution to journal › Article › peer-review
Open AccessFile61 Downloads (Pure)