8 papers
A note on critical problems involving the -Grushin Operator: existence of infinitely many solutions
Paolo Malanchini, Giovanni Molica Bisci, Simone Secchi
We consider a critical problem in a bounded domain involving the -Grushin operator . After a truncation argument, we obtain infinitely many solutions to our problem via K…
Bifurcation and multiplicity results for critical Grushin-Choquard problems
Suman Kanungo, Pawan Kumar Mishra, Giovanni Molica Bisci
We consider the following nonlocal Brézis-Nirenberg type critical Choquard problem involving the Grushin operator \begin{equation*} \left\{ \begin{aligned} -Δ_γ& u =λu + \left(\dis…
Multiple solutions to asymptotically linear problems driven by superposition operators
Danilo Gregorin Afonso, Rossella Bartolo, Giovanni Molica Bisci
In this paper, we investigate the existence and multiplicity of weak solutions to problems involving a superposition operator of the type for a s…
Bifurcation and multiplicity results for critical problems involving the -Grushin operator
Paolo Malanchini, Giovanni Molica Bisci, Simone Secchi
In this article we prove a bifurcation and multiplicity result for a critical problem involving a degenerate nonlinear operator . We extend to a generic a result which…
Gradient regularity for -harmonic functions
Verena Bögelein, Frank Duzaar, Naian Liao +2
We study the local regularity properties of -harmonic functions, i.e. local weak solutions to the fractional -Laplace equation of order in the case $p\in (1,…
Mountain Pass Solutions for an entire semipositone problem involving the Grushin Subelliptic Operator
Giovanni Molica Bisci, Paolo Malanchini, Simone Secchi
For we study the following semipositone problem where is the Grushin operator $$ Δ_ γu(z) = Δ_x u(z) + \ver…
Regularity for the fractional -Laplace equation
Verena Bögelein, Frank Duzaar, Naian Liao +2
Higher Sobolev and Hölder regularity is studied for local weak solutions of the fractional -Laplace equation of order in the case . Depending on the regime considere…
A note on nonlinear critical problems involving the Grushin Subelliptic Operator: bifurcation and multiplicity results
Giovanni Molica Bisci, Paolo Malanchini, Simone Secchi
We consider the boundary value problem $$ \cases{ -Δ_γu = λu + \left\vert u \right\vert^{2^*_γ-2}u &in $Ω$\cr u = 0 &on $\partialΩ$,\cr } $$ where is an open bounded domain in…