Quasilinear problems with critical Sobolev exponent for the Grushin p-Laplace operator
Abstract
Abstract We study the following class of quasilinear degenerate elliptic equations with critical nonlinearity $$\begin{aligned} {\left\{ \begin{array}{ll}-\Delta _{\gamma ,p} u= \lambda |u|^{q-2}u+\left| u\right| ^{p_{\gamma }^{*}-2}u & \text { in } \Omega \subset \mathbb {R}^N,\\ u=0 & \text { on } \partial \Omega , \end{array}\right. } \end{aligned}$$ - Δ γ , p u = λ | u | q - 2 u + u p γ ∗ - 2 u in Ω ⊂ R N , u = 0 on ∂ Ω , where $$\Delta _{\gamma , p}u:=\sum _{i=1}^N X_i(|\nabla _\gamma u|^{p-2}X_i u)$$ Δ γ , p u : = ∑ i = 1 N X i ( | ∇ γ u | p - 2 X i u ) is the Grushin p -Laplace operator, $$z:=(x, y) \in \mathbb {R}^N$$
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Differential Equations and Boundary Problems
Advanced Harmonic Analysis Research
Publication details
- Journal / source
- Nonlinear Differential Equations and Applications NoDEA
- Publisher
- Springer Science and Business Media LLC
- Volume
- 33
- Issue
- 2
- Publication date
- 27 January 2026
- Language
- EN