TY - JOUR
T1 - Strong Instability of Standing Waves for a Type of Hartree Equations
AU - Wang , Chenglin
AU - Zhang , Jian
JO - Journal of Partial Differential Equations
VL - 2
SP - 142
EP - 154
PY - 2025
DA - 2025/06
SN - 38
DO - http://doi.org/10.4208/jpde.v38.n2.2
UR - https://global-sci.org/intro/article_detail/jpde/24213.html
KW - Hartree equation, standing wave, variational arguments, strong instability, blowup.
AB - <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>