A note on nonlinear critical problems involving the Grushin Subelliptic Operator: bifurcation and multiplicity results
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| Format: | Preprint |
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2024
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| _version_ | 1866909121586921472 |
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| author | Bisci, Giovanni Molica Malanchini, Paolo Secchi, Simone |
| author_facet | Bisci, Giovanni Molica Malanchini, Paolo Secchi, Simone |
| contents | We consider the boundary value problem $$
\cases{
-Δ_γu = λu + \left\vert u \right\vert^{2^*_γ-2}u &in $Ω$\cr
u = 0 &on $\partialΩ$,\cr }
$$ where $Ω$ is an open bounded domain in $\mathbb{R}^N$, $N \geq 3$, while $Δ_γ$ is the Grushin operator $$ Δ_ γu(z) = Δ_x u(z) + \vert x \vert^{2γ} Δ_y u (z) \quad (γ\ge 0). $$ We prove a multiplicity and bifurcation result for this problem, extending the results of Cerami, Fortunato and Struwe and of Fiscella, Molica Bisci and Servadei. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_17476 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on nonlinear critical problems involving the Grushin Subelliptic Operator: bifurcation and multiplicity results Bisci, Giovanni Molica Malanchini, Paolo Secchi, Simone Analysis of PDEs We consider the boundary value problem $$ \cases{ -Δ_γu = λu + \left\vert u \right\vert^{2^*_γ-2}u &in $Ω$\cr u = 0 &on $\partialΩ$,\cr } $$ where $Ω$ is an open bounded domain in $\mathbb{R}^N$, $N \geq 3$, while $Δ_γ$ is the Grushin operator $$ Δ_ γu(z) = Δ_x u(z) + \vert x \vert^{2γ} Δ_y u (z) \quad (γ\ge 0). $$ We prove a multiplicity and bifurcation result for this problem, extending the results of Cerami, Fortunato and Struwe and of Fiscella, Molica Bisci and Servadei. |
| title | A note on nonlinear critical problems involving the Grushin Subelliptic Operator: bifurcation and multiplicity results |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2402.17476 |