Geodesic
On capacitary characteristics of noncompact Riemannian manifolds
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2021), pp. 67-75

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In this paper we introduce the concept of $L$-massive subsets of non-compact Riemannian manifolds, also their properties are studied. It is proved that non-trivial bounded solution of considered equation exists on non-compact Riemannian manifold if and only if there is $L$-massive set on it. Also proved similar statement for solutions of semilinear equations with finite energy integral.
Keywords: semilinear equation, energy integral, massive sets
Mots-clés : Liouville type theorem. 
@article{IVM_2021_3_a5,
     author = {A. G. Losev and V. V. Filatov},
     title = {On capacitary characteristics of noncompact {Riemannian} manifolds},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {67--75},
     publisher = {mathdoc},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2021_3_a5/}
}
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A. G. Losev; V. V. Filatov. On capacitary characteristics of noncompact Riemannian manifolds. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2021), pp. 67-75. http://geodesic.mathdoc.fr/item/IVM_2021_3_a5/