Asymptotics for Maxwell–Chern–Simons multivortices

Asymptotics for some nonlinear elliptic systems in Maxwell-Chern-Simons vortex theory

“…In [11] we provided a rigorous proof of this formal argument, in any relevant norm. Namely, we showed…”

Multiple vortices for a self-dual CP(1) Maxwell-Chern-Simons model

“…In particular, u 0 is a local minimum for I 0 in the C 1 -topology. By the Brezis and Nirenberg argument in [3], u 0 is a local minimum for I 0 in the H 1 -topology and thus it is in fact a solution for (16). Now we are ready to prove the following crucial strict inequality:…”

“…Such aC exists by (f 1) since σ + u * is bounded below on M . We claim that for all λ sufficiently large,ū is a supersolution for (16). Indeed, if…”

“…We note that solutions to (16) correspond to critical points in H 1 for the functional I 0 defined by…”

“…13,2007 Multiple vortices for a self-dual CP (1) Maxwell-Chern-Simons model 571 Lemma 2.2 There exists a subsolution u 0 ∈ H 1 for equation (16) such that u ε u 0 weakly in H 1 , strongly in L p for every p ≥ 1 and a.e. on M .…”