Year: 2025
Author: Chenglin Wang, Jian Zhang
Journal of Partial Differential Equations, Vol. 38 (2025), Iss. 2 : pp. 141–153
Abstract
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 $1 < p < 5.$ 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 $ω>0.$
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v38.n2.2
Journal of Partial Differential Equations, Vol. 38 (2025), Iss. 2 : pp. 141–153
Published online: 2025-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: Hartree equation standing wave variational arguments strong instability blowup.