We prove the existence of multiple nontrivial solutions for degenerate elliptic critical growth problems of the form \begin{align*} \begin{cases}-\Delta_{\gamma,p} u= \lambda |u|^{r-2}u+\abs{u}^{p_{\gamma}^{*}-2}u & \text{ in } \Omega %\ \ \Omega\cap \{x=0\}\neq \emptyset, \\ u=0 & \text{ on } \partial \Omega, \end{cases} \end{align*} where $\Delta_{\gamma, p}$ denotes the Grushin $p$-Laplace operator, $\Omega \subset \mathbb{R}^{N}$ is a bounded domain intersecting the degeneration set of the operator, $\lambda>0$ and $p
Multiplicity results for critical growth problems involving the p-Grushin operator
Loiudice A.
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2026-01-01
Abstract
We prove the existence of multiple nontrivial solutions for degenerate elliptic critical growth problems of the form \begin{align*} \begin{cases}-\Delta_{\gamma,p} u= \lambda |u|^{r-2}u+\abs{u}^{p_{\gamma}^{*}-2}u & \text{ in } \Omega %\ \ \Omega\cap \{x=0\}\neq \emptyset, \\ u=0 & \text{ on } \partial \Omega, \end{cases} \end{align*} where $\Delta_{\gamma, p}$ denotes the Grushin $p$-Laplace operator, $\Omega \subset \mathbb{R}^{N}$ is a bounded domain intersecting the degeneration set of the operator, $\lambda>0$ and $pFile in questo prodotto:
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