Fractional Kirchhoff-Choquard system with upper critical exponent and singular nonlinearity

被引：0
作者：
Yanbin Sang
Tsing-San Hsu
机构：
[1] North University of China,Department of Mathematics, School of Science
[2] Chang Gung University,Department of Natural Sciences in the Center for General Education
来源：
Journal of Pseudo-Differential Operators and Applications | 2022年 / 13卷
关键词：
Fractional operator; Kirchhoff system; Upper critical exponent; Singular term; Choquard equation; 35J60; 35J75; 35A15;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we consider a fractional critical Kirchhoff-Choquard system involving singular nonlinearity and the parameter λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda $$\end{document}. By the decomposition of Nehari manifold, we prove that above system admits at least two nontrivial solutions when λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda $$\end{document} satisfies certain condition.
引用
收藏
相关论文
共 68 条
  • [1] Ambrosio V(2020)Existence and concentration of positive solutions for Ann. Math. Pura Appl. 199 317-344
  • [2] Figueiredo GM(2012)-fractional Schrödinger equations J. Differ. Equ. 252 6133-6162
  • [3] Isernia T(1983)On some critical problems for the fractional Laplacian operator Proc. Am. Math. Soc. 88 486-490
  • [4] Barrios B(2016)A relation between pointwise convergence of functions and convergence of functionals Adv. Nonlinear Stud. 16 821-842
  • [5] Colorado E(2004)Critical nonlocal systems with concave-convex powers J. Math. Anal. Appl. 295 225-236
  • [6] de Pablo A(2015)Best constants for Sobolev inequalities for higher order fractional derivatives Math. Models Methods Appl. Sci. 25 1447-1476
  • [7] Sánchez U(2017)On fractional Choquard equations Manuscr. Math. 153 183-230
  • [8] Brézis H(2019)Bifurcation results for a fractional elliptic equation with critical exponent in Milan J. Math. 87 201-231
  • [9] Lieb E(2019)Nehari manifold for fractional Kirchhoff systems with critical nonlinearity Nonlinear Anal. 186 6-32
  • [10] Chen WJ(2017)The Nehari manifold for fractional Kirchhoff problems involving singular and critical terms J. Math. Anal. Appl. 448 1006-1041
1234567