Electron. J. Differential Equations, Vol. 2022 (2022), No. 11, pp. 1-29.

Localized nodal solutions for semiclassical quasilinear Choquard equations with subcritical growth

Bo Zhang, Xiangqing Liu

Abstract:
In this article, we study the existence of localized nodal solutions for semiclassical quasilinear Choquard equations with subcritical growth

where $N\geq 3$, $1<p<N$, $0<\alpha<\min\{2p,N-1\}$, $p<q<p_\alpha^*$, $p_\alpha^*= \frac{p(2N-\alpha)}{2(N-p)}$, V is a bounded function. By the perturbation method and the method of invariant sets of descending flow, for small $\varepsilon$ we establish the existence of a sequence of localized nodal solutions concentrating near a given local minimum point of the potential function V.

Submitted September 6, 2021. Published February 10, 2022.
Math Subject Classifications: 35B20, 35B40.
Key Words: Quasilinear Choquard equation; nodal solutions; perturbation method.
DOI: https://doi.org/10.58997/ejde.2022.11

Show me the PDF file (459 KB), TEX file for this article.

  Bo Zhang
Department of Mathematics
Yunnan Normal University
Kunming, Yunnan 650500, China
email: zhangbo371013@163.com
Xiangqing Liu
Department of Mathematics
Yunnan Normal University
Kunming, Yunnan 650500, China
email: lxq8u8@163.com

Return to the EJDE web page