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

Shao, Liuyang ¹ ; Chen, Haibo ² ; Wang, Yingmin ¹

¹ School of Mathematics and Statistics, GuiZhou University of Finance and Economics, Guiyang, Guizhou 550025, P. R. China
² School of Mathematics and Statistics, Central South University, Changsha, Hunan, 410083, P. R. China

Journal of nonlinear sciences and its applications, Tome 14 (2021) no. 6, p. 390-399.

Résumé

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,\in\mathbb{R}^{N}, \end{cases} $

where $I_{\alpha}$ is a Riesz potential, $0\alpha$, and $\frac{N+\alpha}{N}$, 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.

Détail

DOI : 10.22436/jnsa.014.06.02

Classification : 35B09, 35J20
Keywords: Quasilinear equation, variational methods, ground state solution, Choquard type

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