My research is in the Analysis of Nonlinear Partial Differential Equations (PDEs).
It is focussed on the fundamental questions of existence, non-existence, and structure of solution sets
of nonlinear elliptic equations and inequalities.
Recently I was mostly working on nonlinear Schrödinger type equations with nonlocal interactions,
such as Choquard-Pekar (Schrödinger-Newton) equations, Schrödinger-Poisson type equations,
nonlocal Hartree type equations arising in the density functional theory models for graphene.
The common mathematical feature of all these models is that, unlike in the case of classical local PDEs,
nonlocal terms are present in the equations via Coulombian type interactions or via a fractional Laplacian term, or both.
The tools employed are from the Calculus of Variations, elliptic PDEs theory and Potential Theory.
My earlier research interests were in the area of topological and variational methods of Nonlinear Analysis,
in particular in Critical Points Theory, infinite dimensional Morse Theory and
applications to nonlinear elliptic equations and nonlinear problems
associated with non-local integral operators.
I am always interested to hear from candidates for a PhD or a postdoctoral position in the area of Nonlinear PDEs.
My undergraduate teaching portfolio consists of a broad variety of courses in Analysis and Differential Equations.
In the recent years I held several key administrative roles within the department. I am also involved in several external editorial and research advisory roles.
Swansea SA2 8PP