We prove a multiplicity result for the inhomogeneous subelliptic problem (formula presented) is a sub-Laplacian on a Carnot group (formula presented) is the critical Sobolev exponent in this context, Ω is a bounded domain of G and f is small in a suitable sense. Precisely, we prove the existence of two distinct solutions, that are positive if f is. We adapt to the present subelliptic setting the well-known technique developed by Tarantello (Ann Inst H Poincarè Anal Non Linéaire 9:281–309, 1992).
A multiplicity result for a non-homogeneous subelliptic problem with Sobolev exponent
Loiudice A.
2020-01-01
Abstract
We prove a multiplicity result for the inhomogeneous subelliptic problem (formula presented) is a sub-Laplacian on a Carnot group (formula presented) is the critical Sobolev exponent in this context, Ω is a bounded domain of G and f is small in a suitable sense. Precisely, we prove the existence of two distinct solutions, that are positive if f is. We adapt to the present subelliptic setting the well-known technique developed by Tarantello (Ann Inst H Poincarè Anal Non Linéaire 9:281–309, 1992).File in questo prodotto:
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