Some remarks on the linearized operator about the radial solution for the Ginzburg–Landau equation

✍ Scribed by Anne Beaulieu

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 343 KB
• Volume: 54
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/s0362-546x(03)00128-7

✦ Synopsis

We consider the linearized operators, denoted L d; 1 , of the Ginzburg-Landau operator u + u(1 -|u| 2 ) in R 2 , about the radial solutions u d; 1 (x) = f d (r)e id , for all d ¿ 1. We state the correspondence between the real vector space of the bounded solutions of the equation L d; 1 w=0 and the eigenvalues of the linearized operators of the equations u + 1= 2 u(1 -|u| 2 ) = 0, in B(0; 1), about the radial solutions u d; (x) = f d (r= )e id , that tend to 0 as tends to 0.