About me

I am a Professor at Mathematics Department, Swansea University.

My research is in the Analysis of Nonlinear Partial Differential Equations (PDEs). It is focused on the fundamental questions of existence, non-existence, and structure of solution sets of nonlinear elliptic equations and inequalities. Recently I was 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.

Department of Mathematics
Computational Foundry
College of Science
Swansea University
Fabian Way
Swansea SA1 8EN
Wales, UK

+44 (0)1792 602763
Office: 306 CoFo

My MathSciNet profile    My Google Scholar profile    My ResearchGate profile    My ResearchGate profile