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 Fingerprint is based on mining the text of the person's scientific documents to create an index of weighted terms, which defines the key subjects of each individual researcher.

Boundary Value Problem
Mathematics

P-Laplacian
Mathematics

Eigenvalue
Mathematics

Sturm-Liouville Problem
Mathematics

Jumping Nonlinearities
Mathematics

Global Bifurcation
Mathematics

Nontrivial Solution
Mathematics

Positive Solution
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., 14 Feb 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

Global Asymptotic Stability

P-Laplacian

Positive Solution

Globally Asymptotically Stable

Boundary Value Problem

## 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

## 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

## Simple bifurcation and global curves of solutions of p-Laplacian problems with radial symmetry

Rynne, B. P., 15 Sep 2017, In : Journal of Differential Equations. 263, 6, p. 3611–3626 16 p.Research output: Contribution to journal › Article

Open Access

File