Electron. J. Differential Equations, Vol. 2025 (2025), No. 117, pp. 1-17.

Construction of single-peak solutions for Grushin equations via reduction method

Yawei Wei, Xiaodong Zhou

Abstract:
In this article, we construct single-peak solutions for a class of Grushin equations by using the Lyapunov-Schmidt reduction method, whose concentration points locate on some special critical points of the potential function.

Submitted April 6, 2025. Published December 18, 2025.
Math Subject Classifications: 35J70, 35B40, 35B44.
Key Words: Grushin equation; single-peak solution; Pohozaev identities; Lyapunov-Schmidt reduction.
DOI: 10.58997/ejde.2025.117

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Yawei Wei
School of Mathematical Sciences and LPMC
Nankai University
Tianjin 300071, China
email: weiyawei@nankai.edu.cn
Xiaodong Zhou
School of Mathematical Sciences
Nankai University
Tianjin 300071, China
email: 1120210030@mail.nankai.edu.cn

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