Semiclassical limit for Schrodinger equations with a magnetic field and Hartree-type nonlinearities

Marco Squassina

doi:10.1017/S0308210509000584

Semiclassical limit for Schrodinger equations with a magnetic field and Hartree-type nonlinearities

Marco Squassina

Research output: Contribution to journal › Article › peer-review

92 Citations (Scopus)

Abstract

The semi-classical regime of standing wave solutions of a Schr¨odinger equation in the presence of non-constant electric and magnetic potentials is studied in the case of non-local nonlinearities of Hartree type. It is shown that there exists a family of solutions having multiple concentration regions which are located around the minimum points of the electric potential.

Original language	English
Pages (from-to)	973-1009
Number of pages	37
Journal	PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SECTION A. MATHEMATICS
Volume	140
DOIs	https://doi.org/10.1017/S0308210509000584
Publication status	Published - 2010

Keywords

Semiclassical limits

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10.1017/S0308210509000584

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abstract = "The semi-classical regime of standing wave solutions of a Schr¨odinger equation in the presence of non-constant electric and magnetic potentials is studied in the case of non-local nonlinearities of Hartree type. It is shown that there exists a family of solutions having multiple concentration regions which are located around the minimum points of the electric potential.",

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AU - Squassina, Marco

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AB - The semi-classical regime of standing wave solutions of a Schr¨odinger equation in the presence of non-constant electric and magnetic potentials is studied in the case of non-local nonlinearities of Hartree type. It is shown that there exists a family of solutions having multiple concentration regions which are located around the minimum points of the electric potential.

KW - Semiclassical limits

UR - http://hdl.handle.net/10807/89960

U2 - 10.1017/S0308210509000584

DO - 10.1017/S0308210509000584

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EP - 1009

JO - PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SECTION A. MATHEMATICS

JF - PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SECTION A. MATHEMATICS

ER -

Semiclassical limit for Schrodinger equations with a magnetic field and Hartree-type nonlinearities

Abstract

Keywords

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