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Main Authors:	Wu, Wenju, Zhong, Fulin
Format:	Preprint
Published:	2025
Subjects:	Analysis of PDEs
Online Access:	https://arxiv.org/abs/2504.05972
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author	Wu, Wenju Zhong, Fulin
author_facet	Wu, Wenju Zhong, Fulin
contents	We study a Grushin critical problem in a strip domain which satisfies the periodic boundary conditions. By applying the finite-dimensional reduction method, we construct a periodic solution when the prescribed curvature function is periodic. Furthermore, we also consider the Grushin critical problem in $\mathbb{R}^{N} (N \geq 5)$. Compared with Billel et al. (Differential Integral Equations 32: 49-90, 2019), we use the method by Guo and Yan (Math. Ann. 388: 795-830, 2024) to construct periodic solutions under some weaker conditions, avoiding the complicated estimates and uniqueness proof. Notably, Guo and Yan (Math. Ann. 388: 795-830, 2024) obtained solutions periodic with respect to some of the first variables, while the solutions in this paper are periodic with respect to some intermediate variables.
format	Preprint
id	arxiv_https___arxiv_org_abs_2504_05972
institution	arXiv
publishDate	2025
record_format	arxiv
spellingShingle	Existence of periodic solutions for the Grushin critical problem Wu, Wenju Zhong, Fulin Analysis of PDEs We study a Grushin critical problem in a strip domain which satisfies the periodic boundary conditions. By applying the finite-dimensional reduction method, we construct a periodic solution when the prescribed curvature function is periodic. Furthermore, we also consider the Grushin critical problem in $\mathbb{R}^{N} (N \geq 5)$. Compared with Billel et al. (Differential Integral Equations 32: 49-90, 2019), we use the method by Guo and Yan (Math. Ann. 388: 795-830, 2024) to construct periodic solutions under some weaker conditions, avoiding the complicated estimates and uniqueness proof. Notably, Guo and Yan (Math. Ann. 388: 795-830, 2024) obtained solutions periodic with respect to some of the first variables, while the solutions in this paper are periodic with respect to some intermediate variables.
title	Existence of periodic solutions for the Grushin critical problem
topic	Analysis of PDEs
url	https://arxiv.org/abs/2504.05972

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