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.

## Fingerprint Dive into the research topics where Bryan Patrick Rynne is active. These topic labels come from the works of this person. Together they form a unique fingerprint.

Boundary Value Problem
Mathematics

P-Laplacian
Mathematics

Eigenvalue
Mathematics

Sturm-Liouville Problem
Mathematics

Jumping Nonlinearities
Mathematics

Nontrivial Solution
Mathematics

Global Bifurcation
Mathematics

Sturm-Liouville
Mathematics

## Research Output 1990 2019

## 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

## 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

Open Access

File

Global Asymptotic Stability

G-function

P-Laplacian

Asymptotic stability

Boundary value problems

## Linearized stability implies asymptotic stability for radially symmetric equilibria of *p*-Laplacian boundary value problems in the unit ball in ℝ^{N}

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

Open Access

File

P-Laplacian

Unit ball

Asymptotic Stability

Principal Eigenvalue

Trivial

## Linearized stability implies dynamic stability for equilibria of 1-dimensional, p-Laplacian boundary value problems

Rynne, B. P., 29 Jan 2019, In : Proceedings of the Royal Society of Edinburgh, Section A: Mathematics.Research output: Contribution to journal › Article

Open Access

File

## Global stability, or instability, of positive equilibria of p-Laplacian boundary value problems with p-convex nonlinearities

Rynne, B. P., 2017, In : Rendiconti dell'Istituto di Matematica dell'Universita di Trieste: an International Journal of Mathematics. 49, p. 193-206 14 p.Research output: Contribution to journal › Article

Open Access

File