Existence of periodic solutions for the Grushin critical problem
Abstract
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 consider the Grushin critical problem in RN(N≥5). Compared with [B. Gheraibia, C. Wang and J. Yang, Differ. Integral Equations 32, 49–90 (2019)], we use the method of [Y. Guo and S. Yan, Math. Ann. 388, 795–830 (2024)] to construct periodic solutions under some weaker conditions, avoiding the complicated estimates and uniqueness proof.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Geometric Analysis and Curvature Flows
Stability and Controllability of Differential Equations
Publication details
- Journal / source
- Journal of Mathematical Physics
- Volume
- 67
- Issue
- 6
- Publication date
- 1 June 2026
- Language
- EN