Paolo Malanchini

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20242026

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math.AP2024

Mountain Pass Solutions for an entire semipositone problem involving the Grushin Subelliptic Operator

Giovanni Molica Bisci, Paolo Malanchini, Simone Secchi

For $N \geq 3$ we study the following semipositone problem $- Δ_{γ} u = g (z) f_{a} (u) in R^{N},$ where $Δ_{γ}$ is the Grushin operator $$ Δ_ γu(z) = Δ_x u(z) + \ver…

math.AP2024

A note on nonlinear critical problems involving the Grushin Subelliptic Operator: bifurcation and multiplicity results

Giovanni Molica Bisci, Paolo Malanchini, Simone Secchi

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…