CONSTRAINED SCHRODINGER-POISSON SYSTEM WITH NON-CONSTANT INTERACTION

Autor(es)

Pisani, Lorenzo ^[1] ; Siciliano, Gaetano ^[2]

Afiliação do(s) autor(es)

^[1] Univ Bari Aldo Moro, Dipartimento Matemat, I-70125 Bari - Italy

^[2] Univ Fed Abc, CMCC, BR-09210170 Santo Andre, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS; v. 15, n. 1 FEB 2013.
• Citações Web of Science: 3

Resumo

In this paper we are dealing with a Schrodinger-Maxwell system in a bounded domain of R-3; the unknowns are the charged standing waves psi = e-(i omega t)u(x) in equilibrium with a purely electrostatic potential phi. The system is not autonomous, in the sense that the coupling depends on a function q = q(x). The non-homogeneous Neumann boundary condition on phi prescribes the flux of the electric field F and gives rise to a necessary condition. On the other hand we consider the usual normalizing condition in L-2 for u. Under mild assumptions involving F and the function q = q(x), we prove that this problem has a variational framework: its solutions can be characterized as constrained critical points. Then, by means of the Ljusternick-Schnirelmann theory, we get the existence of infinitely many solutions. (AU)

• Processo FAPESP: 11/21362-2 - Ações de grupos, teoria de subvariedades, e análise global em geometria Riemanniana e pseudo-riemanniana
• Beneficiário: Paolo Piccione
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 11/01081-9 - Problemas variacionais geométricos e EDPs
• Beneficiário: Paolo Piccione
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional