A topological join construction and the Toda system on compact surfaces of arbitrary genus

which arises as a model for nonabelian Chern–Simons vortices. Here $h_{1}$ and $h_{2}$ are smooth positive functions and $ρ_{1}$ and $ρ_{2}$ two positive parameters.

For the first time, the ranges $ρ_{1} \in (4 k π, 4 (k + 1) π)$ , $k \in ℕ$ , and $ρ_{2} \in (4 π, 8 π)$ are studied with a variational approach on surfaces with arbitrary genus. We provide a general existence result by using a new improved Moser–Trudinger-type inequality and introducing a topological join construction in order to describe the interaction of the two components $u_{1}$ and $u_{2}$ .

Keywords

geometric PDEs, variational methods, min-max schemes

Mathematical Subject Classification 2010

Primary: 35J50, 35J61, 35R01

Milestones

Received: 19 March 2015

Accepted: 7 September 2015

Published: 23 December 2015

Authors

Aleks Jevnikar
Mathematics Scuola Internazionale Superiore di Studi Avanzati Via Bonomea 265 I-34136 Trieste Italy

Sadok Kallel
American University of Sharjah University City 26666 Sharjah United Arab Emirates	Laboratoire Painlevé Université de Lille 1 Cité scientifique Batiment M2 59655 Villeneuve d’Ascq France

Andrea Malchiodi
Department of Mathematics Scuola Normale Superiore Piazza dei Cavalieri 7 I-50126 Pisa Italy

Vol. 8, No. 8, 2015

Aleks Jevnikar, Sadok Kallel and Andrea Malchiodi

Abstract

Keywords

Mathematical Subject Classification 2010

Milestones

Authors