Hamiltonian elliptic systems: a guide to variational frameworks

  • Denis Bonheure

    Université libre de Bruxelles, Belgium
  • Ederson Moreira dos Santos

    Universidade de São Paulo, Sao Carlos, Brazil
  • Hugo Tavares

    IST - Universidade de Lisboa, Portugal


Consider a Hamiltonian elliptic system of type

where is a power-type nonlinearity, for instance , having subcritical growth, and is a bounded domain of , . The aim of this paper is to give an overview of the several variational frameworks that can be used to treat such a system. Within each approach, we address existence of solutions, and in particular of ground state solutions. Some of the available frameworks are more adequate to derive certain qualitative properties; we illustrate this in the second half of this survey, where we also review some of the most recent literature dealing mainly with symmetry, concentration, and multiplicity results. This paper contains some original results as well as new proofs and approaches to known facts.

Cite this article

Denis Bonheure, Ederson Moreira dos Santos, Hugo Tavares, Hamiltonian elliptic systems: a guide to variational frameworks. Port. Math. 71 (2014), no. 3/4, pp. 301–395

DOI 10.4171/PM/1954