@Article{JPDE-38-142,
author = {Wang , Chenglin and Zhang , Jian},
title = {Strong Instability of Standing Waves for a Type of Hartree Equations},
journal = {Journal of Partial Differential Equations},
year = {2025},
volume = {38},
number = {2},
pages = {142--154},
abstract = {<p style="text-align: justify;">In this paper, we study the following three-dimensional Schrödinger equation with combined Hartree-type and power-type nonlinearities $$i\partial_t\psi+\Delta\psi+(|x|^{-2}*|\psi|^2)\psi+|\psi|^{p-1}\psi=0$$with $1 &lt; p &lt; 5.$ Using standard variational arguments, the existence of ground state
solutions is obtained. And then we prove that when $p≥3,$ the standing wave solution $e^{ iωt}u_ω(x)$ is strongly unstable for the frequency $ω&gt;0.$</p>},
issn = {2079-732X},
doi = {https://doi.org/10.4208/jpde.v38.n2.2},
url = {http://global-sci.org/intro/article_detail/jpde/24213.html}
}