Existence and asymptotic behavior of normalized solutions for Kirchhoff equation with Hardy nonlinearities
Year: 2026
Type: article
Abstract: In this paper, we consider the qualitative analysis of solutions for the following Kirchhoff equation with Hardy nonlinearities: $$ \left \{\begin{aligned} &-(a+b\int _{\mathbb{R}^{N}}|\nabla u|^{2} dx)\Delta u=\lambda u+\frac{|u|^{p - 2}u}{|x|^{\beta}}+\mu \frac{|u|^{q - 2}u}{|x|^{\beta}}, &&\text{ in } \mathbb{R}^{N},\\ &\int _{\mathbb{R}^{N}} u^{2} dx = c^{2}, \end{aligned}\right . $$ where $N\geq 3,~0<\beta <2,~2 0,~\mu >0$ and $\lambda \in \mathbb{R}$ appears as a Lagrange multiplier. By developing a perturbed Pohozaev constraint approach, we show the existence of normalized solutions under the mixed $L^{2}$-critical case where $2< q<\frac{2(N+4-\beta )}{N}<p<2^{*}_{\beta}$ and ground state solutions in the $L^{2}$-supercritical case where $\frac{2(N+4-\beta )}{N}< q< p<2^{*}_{\beta}$, respectively. Moreover, the asymptotic behaviors of the normalized solutions are also obtained.
Source: Boundary Value Problems
Authors: Yufei Wang, Yang Yang
Institution: Jiangnan University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,890
OpenAlex ID: W7160825104