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
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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
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
- Quasilinear equation
- variational methods
- ground state solution
- Choquard type
MSC
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