Normalized solutions for a fractional $N/s$-Laplacian Choquard equation with exponential critical nonlinearities
Analysis of PDEs
2023-10-26 v2
Abstract
In this paper, we are concerned with the following fractional -Laplacian Choquard equation \begin{align*} \begin{cases} (-\Delta)^s_{N/s}u=\lambda |u|^{\frac{N}{s}-2}u +(I_\mu*F(u))f(u),\ \ \mbox{in}\ \mathbb{R}^N, \displaystyle\int_{\mathbb{R}^N}|u|^{N/s} \mathrm{d}x=a^{N/s}, \end{cases} \end{align*} where , , is a prescribed constant, , with , is the primitive function of , and is a continuous function with exponential critical growth of Trudinger-Moser type. Under some suitable assumptions on , we prove that the above problem admits a ground state solution for any given , by using the constraint variational method and minimax technique.
Keywords
Cite
@article{arxiv.2310.05477,
title = {Normalized solutions for a fractional $N/s$-Laplacian Choquard equation with exponential critical nonlinearities},
author = {Wenjing Chen and Zexi Wang},
journal= {arXiv preprint arXiv:2310.05477},
year = {2023}
}