Mengrui Luo, Yongyi Lan, Normalized solutions for p-kirchhoff equations with prescribed mass and general nonlinearities, Vol. 2025 (2025), No. 19, pp. 1-18

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DOI: 10.23952/jnfa.2025.19

Received January 16, 2025; Accepted May 20, 2025; Published June 25, 2025

Abstract. In this paper, we study the existence of normalized solutions to the following $p$ -Kirchhoff equation

$-(a+b \int_{R^3} |\nabla u|^pdx) \Delta_p u+\lambda u=g(u),$ in $R^3,$
$\int_{R^3} |u|^2dx =m,$

where $a>0,b\geq0,$ and $m>0$ are constants, $p^*=\frac{Np}{N-p}$ is the critical Sobolev exponent, $\lambda$ is a Lagrange multiplier, $\Delta_pu=div(|\nabla u|^{p-2}\nabla u)$ , $2\textless p\textless N=3$ , and the nonlinear term $g$ satisfies certain conditions. Under the right conditions, we study that the $p$ -Kirchhoff equation has a positive normalized solution $(\lambda,u_\lambda)\in(0,+\infty)\times W^{1,p}_{rad}(\mathbb{R}^3)$ for any $m>0$ .

How to Cite this Article:
M. Luo, Y. Lan, Normalized solutions for p-kirchhoff equations with prescribed mass and general nonlinearities, J. Nonlinear Funct. Anal. 2025 (2025) 19.