Multiple solutions to a magnetic nonlinear Choquard equation
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- 作者：Silvia Cingolani (1)
Mónica Clapp (2)
Simone Secchi (3) - 关键词：35Q55 ; 35Q40 ; 35J20 ; 35B06 ; Nonlinear Choquard equation ; Nonlocal nonlinearity ; Electromagnetic potential ; Multiple solutions ; Intertwining solutions
- 刊名：Zeitschrift f眉r angewandte Mathematik und Physik
- 出版年：2012
- 出版时间：April 2012
- 年：2012
- 卷：63
- 期：2
- 页码：233-248
- 全文大小：305KB
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Mónica Clapp (2)
Simone Secchi (3)
1. Dipartimento di Matematica, Politecnico di Bari, via Orabona 4, 70125, Bari, Italy
2. Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, C.U., 04510, México D.F., Mexico
3. Dipartimento di Matematica ed Applicazioni, Università di Milano-Bicocca, via Cozzi 53, 20125, Milano, Italy - ISSN：1420-9039
文摘
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?). 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.