English

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 N/sN/s-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 s(0,1)s\in(0,1), 1<NsN+1<\frac{N}{s}\in \mathbb{N}^+, a>0a>0 is a prescribed constant, λR\lambda\in \mathbb{R}, Iμ(x)=1xμI_\mu(x)=\frac{1}{|x|^{\mu}} with μ(0,N)\mu\in(0,N), FF is the primitive function of ff, and ff is a continuous function with exponential critical growth of Trudinger-Moser type. Under some suitable assumptions on ff, we prove that the above problem admits a ground state solution for any given a>0a>0, 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}
}