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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.

MSC:

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
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Full Text: Euclid