Multiple solutions to a magnetic nonlinear Choquard equation

Details Multiple solutions to a magnetic nonlinear Choquard equation Multiple solutions to a magnetic nonlinear Choquard equation

2011-09-07

arxiv.org/abs/1109.1386v1

Mathematics

Analysis of PDEs

To appear on ZAMP

Scientific paper

We consider the stationary nonlinear magnetic Choquard equation [(-\mathrm{i}\nabla+A(x))^{2}u+V(x)u=(\frac{1}{|x|^{\alpha}}\ast |u|^{p}) |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$,$ $N\geq3$, $\alpha\in(0,N)$ and $2-(\alpha/N)

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