Translator Disclaimer
January/February 2019 Existence and local uniqueness of bubbling solutions for the Grushin critical problem
Billel Gheraibia, Chunhua Wang, Jing Yang
Differential Integral Equations 32(1/2): 49-90 (January/February 2019).

Abstract

In this paper, we study the following Grushin critical problem $$ -\Delta u(x)=\Phi(x)\frac{u^{\frac{N}{N-2}}(x)} {|y|},\,\,\,\,u>0,\,\,\,\text{in}\,\,\,\mathbb R^{N}, $$ where $x=(y,z)\in\mathbb R^{k}\times \mathbb R^{N-k},N\geq 5,\Phi(x)$ is positive and periodic in its the $\bar{k}$ variables $(z_{1},...,z_{\bar{k}}),1\leq \bar{k} < \frac{N-2}{2}.$ Under some suitable conditions on $\Phi(x)$ near its critical point, we prove that the problem above has solutions with infinitely many bubbles. Moreover, we also show that the bubbling solutions obtained in our existence result are locally unique. Our result implies that some bubbling solutions preserve the symmetry from the potential $\Phi(x).$

Citation

Download Citation

Billel Gheraibia. Chunhua Wang. Jing Yang. "Existence and local uniqueness of bubbling solutions for the Grushin critical problem." Differential Integral Equations 32 (1/2) 49 - 90, January/February 2019.

Information

Published: January/February 2019
First available in Project Euclid: 11 December 2018

zbMATH: 07031709
MathSciNet: MR3909979

Subjects:
Primary: 35B40, 35B45, 35J40

Rights: Copyright © 2019 Khayyam Publishing, Inc.

JOURNAL ARTICLE
42 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.32 • No. 1/2 • January/February 2019
Back to Top