On the Grushin critical problem with a cylindrical symmetry. (English) Zbl 1311.35169

Summary: By a Lyapunov-Schmidt reduction argument, for a type of Grushin critical problem with cylindrical symmetry, we prove that it has infinitely many positive solutions with cylindrical symmetry, whose energy can be made arbitrarily large.


35M10 PDEs of mixed type
35B40 Asymptotic behavior of solutions to PDEs
35B45 A priori estimates in context of PDEs
35J40 Boundary value problems for higher-order elliptic equations
Full Text: Euclid