Ground state solutions for a class of quasilinear Choquard equation with critical growth

Volume 14, Issue 6, pp 390--399 http://dx.doi.org/10.22436/jnsa.014.06.02
Publication Date: May 09, 2021 Submission Date: February 06, 2021 Revision Date: February 27, 2021 Accteptance Date: March 18, 2021

Authors

Liuyang Shao - School of Mathematics and Statistics, GuiZhou University of Finance and Economics, Guiyang, Guizhou 550025, P. R. China. Haibo Chen - School of Mathematics and Statistics, Central South University, Changsha, Hunan, 410083, P. R. China. Yingmin Wang - School of Mathematics and Statistics, GuiZhou University of Finance and Economics, Guiyang, Guizhou 550025, P. R. China.


Abstract

In this paper, we consider the following quasilinear Choquard equation with critical nonlinearity \[ \begin{cases} -\triangle u+V(x)u-u\triangle u^{2}=(I_{\alpha}\ast|u|^{p})|u|^{p-2}u+u^{2(2^{\ast})-2}u,&x\in\mathbb{R}^{N}, \\ u>0,&x\in\mathbb{R}^{N}, \end{cases} \] where \(I_{\alpha}\) is a Riesz potential, \(0<\alpha<N\), and \(\frac{N+\alpha}{N}<p<\frac{N+\alpha}{N-2}\), with \(2^{\ast}=\frac{2N}{N-2}\). Under suitable assumption on \(V\), we research the existence of positive ground state solutions of above equations. Moreover, we consider the ground state solution of the equation (1.4). Our work supplements many existing partial results in the literature.


Share and Cite

  • Share on Facebook
  • Share on Twitter
  • Share on LinkedIn
ISRP Style

Liuyang Shao, Haibo Chen, Yingmin Wang, Ground state solutions for a class of quasilinear Choquard equation with critical growth, Journal of Nonlinear Sciences and Applications, 14 (2021), no. 6, 390--399

AMA Style

Shao Liuyang, Chen Haibo, Wang Yingmin, Ground state solutions for a class of quasilinear Choquard equation with critical growth. J. Nonlinear Sci. Appl. (2021); 14(6):390--399

Chicago/Turabian Style

Shao, Liuyang, Chen, Haibo, Wang, Yingmin. "Ground state solutions for a class of quasilinear Choquard equation with critical growth." Journal of Nonlinear Sciences and Applications, 14, no. 6 (2021): 390--399


Keywords


MSC


References