MMN-2869

Solutions of homogeneous fractional p-Kirchhoff equations in R^N

  • Vu Ho, Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam; Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam, hovu@tdtu.edu.vn
  • Nhat Vy Huynh, Department of Fundamental Sciences, Ho Chi Minh City University of Transport, Ho Chi Minh City, Vietnam; Faculty of Mathematics and Computer Science, University of Science, Vietnam National University-Ho Chi Minh City, Ho Chi Minh City, Vietnam, hmnguon@gmail.com
  • Phuong Le, Department of Mathematical Economics, Banking University of Ho Chi Minh City, Vietnam, phuongl@buh.edu.vn

Abstract

In this note, we give a simple transformation so that solutions of the fractional $p$-Kirchhoff equation in $\mathbb{R}^N$ are easily obtained from known solutions of the corresponding fractional $p$-Laplace equation. As an application, we classify all positive solutions of some (fractional) $p$-Kirchhoff equations with sub-critical or critical nonlinearities and H\'enon-Hardy potentials. Similar results for Kirchhoff type systems are also discussed.


Vol. 20 (2019), No. 2, pp. 957-968
DOI: 10.18514/MMN.2019.2869


Download: MMN-2869