Some results on subelliptic equations. (English) Zbl 1134.35055
Summary: We consider the principal eigenvalue problem for Hörmander’s Laplacian on \(\mathbb R^{n}\), and we find a comparison principle for such principal eigenvalues. We also study a related semi-linear sub-elliptic equation in the whole \(\mathbb R^{n}\) and prove that, under a suitable condition, we have infinitely many positive solutions of the problem.
MSC:
| 35J65 | Nonlinear boundary value problems for linear elliptic equations |
| 35H20 | Subelliptic equations |
References:
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