Abstract
Existence of solution for semilinear problem with the Laplace-Beltrami operator on non-compact Riemannian manifolds with rich symmetries is proved by concentration compactness based on actions of the manifold's isometry group.
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Communicated by David Jerison
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Fieseler, K.H., Tintarev, K. Semilinear elliptic problems and concentration compactness on non-compact Riemannian manifolds. J Geom Anal 13, 67–75 (2003). https://doi.org/10.1007/BF02930997
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DOI: https://doi.org/10.1007/BF02930997