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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

CONSTRAINED SCHRODINGER-POISSON SYSTEM WITH NON-CONSTANT INTERACTION

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Author(s):
Pisani, Lorenzo [1] ; Siciliano, Gaetano [2]
Total Authors: 2
Affiliation:
[1] Univ Bari Aldo Moro, Dipartimento Matemat, I-70125 Bari - Italy
[2] Univ Fed Abc, CMCC, BR-09210170 Santo Andre, SP - Brazil
Total Affiliations: 2
Document type: Journal article
Source: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS; v. 15, n. 1 FEB 2013.
Web of Science Citations: 3
Abstract

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)

FAPESP's process: 11/21362-2 - Group actions, submanifold theory and global analysis in Riemannian and pseudo-Riemannian geometry
Grantee:Paolo Piccione
Support type: Research Projects - Thematic Grants
FAPESP's process: 11/01081-9 - Geometric variational problems and PDEs
Grantee:Paolo Piccione
Support type: Research Grants - Visiting Researcher Grant - International