@article {jevnikar_2016, title = {New existence results for the mean field equation on compact surfaces via degree theory}, journal = {Rend. Sem. Mat. Univ. Padova}, volume = {136}, year = {2016}, pages = {11{\textendash}17}, doi = {10.4171/RSMUP/136-2}, author = {Aleks Jevnikar} } @article {jevnikar2016note, title = {A note on a multiplicity result for the mean field equation on compact surfaces}, journal = {Advanced Nonlinear Studies}, volume = {16}, year = {2016}, pages = {221{\textendash}229}, publisher = {De Gruyter}, doi = {10.1515/ans-2015-5009}, author = {Aleks Jevnikar} } @article {BATTAGLIA2015937, title = {A general existence result for the Toda system on compact surfaces}, journal = {Advances in Mathematics}, volume = {285}, year = {2015}, pages = {937 - 979}, abstract = {

In this paper we consider the following Toda system of equations on a compact surface:-Δu1=2ρ1(h1eu1∫Σh1eu1dVg-1)-ρ2(h2eu2∫Σh2eu2dVg-1)-Δu1=-4π∑j=1mα1,j(δpj-1),-Δu2=2ρ2(h2eu2∫Σh2eu2dVg-1)-ρ1(h1eu1∫Σh1eu1dVg-1)-Δu2=-4π∑j=1mα2,j(δpj-1), which is motivated by the study of models in non-abelian Chern{\textendash}Simons theory. Here h1,h2 are smooth positive functions, ρ1,ρ2 two positive parameters, pi points of the surface and α1,i,α2,j non-negative numbers. We prove a general existence result using variational methods. The same analysis applies to the following mean field equation-Δu=ρ1(heu∫ΣheudVg-1)-ρ2(he-u∫Σhe-udVg-1), which arises in fluid dynamics."

}, keywords = {Geometric PDEs, Min{\textendash}max schemes, Variational methods}, issn = {0001-8708}, doi = {https://doi.org/10.1016/j.aim.2015.07.036}, url = {http://www.sciencedirect.com/science/article/pii/S0001870815003072}, author = {Luca Battaglia and Aleks Jevnikar and Andrea Malchiodi and David Ruiz} } @article {jevnikar2015topological, title = {A topological join construction and the Toda system on compact surfaces of arbitrary genus}, journal = {Analysis \& PDE}, volume = {8}, number = {8}, year = {2015}, pages = {1963{\textendash}2027}, publisher = {Mathematical Sciences Publishers}, doi = {10.2140/apde.2015.8.1963}, author = {Aleks Jevnikar and Kallel, Sadok and Andrea Malchiodi} } @mastersthesis {2015, title = {Variational aspects of Liouville equations and systems}, year = {2015}, note = {The PHD thesis is composed of 112 pages and is recorded in PDF format}, school = {SISSA}, keywords = {Toda system}, author = {Aleks Jevnikar} } @article {jevnikar_2013, title = {An existence result for the mean-field equation on compact surfaces in a doubly supercritical regime}, journal = {Proceedings of the Royal Society of Edinburgh: Section A Mathematics}, volume = {143}, number = {5}, year = {2013}, pages = {1021{\textendash}1045}, publisher = {Royal Society of Edinburgh Scotland Foundation}, doi = {10.1017/S030821051200042X}, author = {Aleks Jevnikar} }