Qualitative study of radial solutions of the Ginzburg-Landau system in RN (N ≥ 3)

Abstract In this work, we are interested in solutions ω : R N → R N , N ≥ 3, to Ginzburg-Landau system −Δω = ω(1 − |ω|2), having the form ω(x) = u(|x|)g( x |x| ) . By using a shootin we prove the existence of three families of profiles u and investigate its properties. In particular, we shall show that, for any admissible function g, there exists a unique positive solution ug which approaches 1 as |x| → +∞.