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  1. Zeitschrift für angewandte Mathematik und Physik
  2. Zeitschrift für angewandte Mathematik und Physik : Volume 63
  3. Zeitschrift für angewandte Mathematik und Physik : Volume 63, Issue 2, April 2012
  4. Multiple solutions to a magnetic nonlinear Choquard equation
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Zeitschrift für angewandte Mathematik und Physik : Volume 67
Zeitschrift für angewandte Mathematik und Physik : Volume 66
Zeitschrift für angewandte Mathematik und Physik : Volume 65
Zeitschrift für angewandte Mathematik und Physik : Volume 64
Zeitschrift für angewandte Mathematik und Physik : Volume 63
Zeitschrift für angewandte Mathematik und Physik : Volume 63, Issue 6, December 2012
Zeitschrift für angewandte Mathematik und Physik : Volume 63, Issue 5, October 2012
Zeitschrift für angewandte Mathematik und Physik : Volume 63, Issue 4, August 2012
Zeitschrift für angewandte Mathematik und Physik : Volume 63, Issue 3, June 2012
Zeitschrift für angewandte Mathematik und Physik : Volume 63, Issue 2, April 2012
Discrete spectrum of a model Schrödinger operator on the half-plane with Neumann conditions
Multiple solutions to a magnetic nonlinear Choquard equation
Properties of traveling waves for integrodifference equations with nonmonotone growth functions
Heat flow method for Lichnerowicz type equations on closed manifolds
MHD oblique stagnation-point flow of a Newtonian fluid
Boundary blow-up solutions of p-Laplacian elliptic equations with lower order terms
First stages of drop impact on a dry surface: asymptotic model
Modeling the join curve between two co-axial carbon nanotubes
Self-diffusion in remodeling and growth
Wave-induced perturbations in cylindrically layered smectic A liquid crystals
Revisiting total, matric, and osmotic suction in partially saturated geomaterials
A remark on global existence of solutions of shadow systems
Zeitschrift für angewandte Mathematik und Physik : Volume 63, Issue 1, February 2012
Zeitschrift für angewandte Mathematik und Physik : Volume 62
Zeitschrift für angewandte Mathematik und Physik : Volume 61
Zeitschrift für angewandte Mathematik und Physik : Volume 60
Zeitschrift für angewandte Mathematik und Physik : Volume 59
Zeitschrift für angewandte Mathematik und Physik : Volume 58
Zeitschrift für angewandte Mathematik und Physik : Volume 57
Zeitschrift für angewandte Mathematik und Physik : Volume 56
Zeitschrift für angewandte Mathematik und Physik : Volume 55
Zeitschrift für angewandte Mathematik und Physik : Volume 54
Zeitschrift für angewandte Mathematik und Physik : Volume 53
Zeitschrift für angewandte Mathematik und Physik : Volume 52
Zeitschrift für angewandte Mathematik und Physik : Volume 51
Zeitschrift für angewandte Mathematik und Physik : Volume 50
Zeitschrift für angewandte Mathematik und Physik : Volume 49
Zeitschrift für angewandte Mathematik und Physik : Volume 48

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Multiple solutions to a magnetic nonlinear Choquard equation

Content Provider SpringerLink
Author Clapp, Mónica Cingolani, Silvia Secchi, Simone
Copyright Year 2011
Abstract We consider the stationary nonlinear magnetic Choquard equation $$(- {\rm i}\nabla+ A(x))^{2}u + V (x)u = \left(\frac{1}{|x|^{\alpha}}\ast |u|^{p}\right) |u|^{p-2}u,\quad x\in\mathbb{R}^{N}$$ where A is a real-valued vector potential, V is a real-valued scalar potential, N ≥ 3, $${\alpha \in (0, N)}$$ and 2 − (α/N) < p < (2N − α)/(N−2). We assume that both A and V are compatible with the action of some group G of linear isometries of $${\mathbb{R}^{N}}$$ . We establish the existence of multiple complex valued solutions to this equation which satisfy the symmetry condition $$u(gx) = \tau(g)u(x)\quad{\rm for\, all }\ g \in G,\;x \in \mathbb{R}^{N},$$ where $${\tau : G \rightarrow \mathbb{S}^{1}}$$ is a given group homomorphism into the unit complex numbers.
Ending Page 248
Page Count 16
Starting Page 233
File Format PDF
ISSN 00442275
e-ISSN 14209039
Journal Zeitschrift für angewandte Mathematik und Physik
Issue Number 2
Volume Number 63
Language English
Publisher SP Birkhäuser Verlag Basel
Publisher Date 2011-10-09
Publisher Place Basel
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Multiple solutions Symmetries, invariants, etc. Mathematical Methods in Physics PDEs in connection with quantum mechanics Nonlinear Choquard equation Electromagnetic potential Variational methods for second-order elliptic equations Nonlocal nonlinearity Intertwining solutions Theoretical and Applied Mechanics NLS-like equations (nonlinear Schrödinger)
Content Type Text
Resource Type Article
Subject Applied Mathematics Physics and Astronomy
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