Hamiltonian elliptic systems: a guide to variational frameworks

By Denis Bonheure, Ederson Moreira dos Santos, Hugo Tavares. 2014

75 citations recorded by the source corpus.

Consider a Hamiltonian elliptic system of type 8 < : u = Hv(u;v) in v = Hu(u;v) in u;v = 0 on @ where H is a power-type nonlinearity, for instance H(u;v) =juj p+1 =(p + 1) +jvj q+1 =(q + 1); having subcritical growth, and is a bounded domain of R N , N 1. 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 proper- ties; we illustrate this in the second half of this survey, where we also review some of the most recent literature dealing mainly with symmetry, concentra- tion, and multiplicity results. This paper contains some original results as well as new proofs and approaches to known facts.

Subfields: Applied Mathematics, Computational Mechanics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/02cb0feaee51f39bb6df54ec4646e94f58860449

Citations in the corpus

• Uniqueness (2021, unknown): “…equation, since with q = 1, u solves the fourth-order elliptic equation Due to their structure, they pose many mathematical challenges, and they can be treated by using several variational frameworks, each one with its advantages and disadvantages (we refer to the survey [19] for more details).”