Multiple normalized solutions to critical Choquard equation involving fractional p-Laplacian in RN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {R}}^{N}$$\end{document}Multiple normalized solutions to critical...X. Zhang et al.

The paper mainly investigates the existence of multiple normalized solutions for critical Choquard equation with involving fractional p-Laplacian in RN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {R}}^{N}$$\end{document}: (-Δ)psu+Z(κx)|u|p-2u=λ|u|p-2u+[1|x|N-α∗|u|q]|u|q-2u+σ|u|ps∗-2uinRN,∫RN|u|pdx=ap,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \left\{ \! \begin{array}{lll} (-\Delta )_{p}^{s}u \!+\!Z(\kappa x)|u|^{p-2}u\!=\!\lambda |u|^{p-2}u\!+\! \Big [\dfrac{1}{|x|^{N-\alpha }}*|u|^{q}\!\Big ]|u|^{q-2}u\!+\!\sigma |u|^{p_{s}^{*}-2}u & \text{ in }\ {\mathbb {R}}^{N}\!, \\ \displaystyle \int _{{\mathbb {R}}^{N}}|u|^{p}dx=a^{p}, \end{array} \right. \end{aligned}$$\end{document}where κ>0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa > 0$$\end{document} is a small parameter, λ∈R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda \in {\mathbb {R}}$$\end{document} is a Lagrange multiplier, Z:RN→[0,∞)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Z:{\mathbb {R}}^{N}\rightarrow [0,\infty )$$\end{document} is a continuous function. Under the right conditions, together with the minimization techniques, truncated method, variational methods and the Lusternik–Schnirelmann category, we obtain the existence of multiple normalized solutions, which can be viewed as a partial extension of the previous results concerning the existence of normalized solutions to this problem in the case of s=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$s = 1$$\end{document}, p=2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p = 2$$\end{document} and subcritical case.