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arXiv · 1610.05503

Nondegeneracy of ground states and multiple semiclassical solutions of the Hartree equation for general dimensions

Guoyuan Chen
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Abstract

We study nondegeneracy of ground states of the Hartree equation $$ -\Delta u+u=(I_{2}\ast u^2)u\quad\mbox{ in }\mathbb R^n $$ where $n=3,4,5$ and $I_2$ is the Newton potential. As an application of the nondegeneracy result, we use a Lyapunov-Schmidt reduction argument to construct multiple semiclassical solutions to the following Hartree equation with an external potential $$-\varepsilon^2\Delta u+u+V(x)u=\varepsilon^{-2}(I_{2}\ast u^2)u\quad \mbox{ in }\mathbb R^n.$$

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Guoyuan Chen. 2016-10-18. Nondegeneracy of ground states and multiple semiclassical solutions of the Hartree equation for general dimensions. https://arxiv.org/abs/1610.05503

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