Year: 2024
Author: Yuan Xu, Yongyi Lan
Journal of Mathematical Study, Vol. 57 (2024), Iss. 4 : pp. 509–527
Abstract
In this paper, for given mass $c>0,$ we study the existence of normalized solutions to the following nonlinear Kirchhoff equation $$\begin{cases} (a+b\int_{\mathbb{R}^3}[|\nabla u|^2+V(x)u^2]dx)[-\Delta u+V(x)u]=\lambda u+\mu|u|^{q-2}u+|u|^{p-2}u, \ \ \ {\rm in}\ \ \mathbb{R}^3, \\ \int_{\mathbb{R}^3}|u|^2dx=c^2, \end{cases}$$where $a>0, b>0, λ∈\mathbb{R},$ $5<q< p<6,$ $\mu>0$ and $V$ is a continuous non-positive function vanishing at infinity. Under some mild assumptions on $V,$ we prove the existence of a mountain pass normalized solution via the minimax principle.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v57n4.24.08
Journal of Mathematical Study, Vol. 57 (2024), Iss. 4 : pp. 509–527
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Kirchhoff equation normalized solutions minimax principle.