On capacitary characteristics of noncompact Riemannian manifolds

A. G. Losev ; V. V. Filatov

Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2021), pp. 67-75.

Résumé

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.

Détail

Keywords: semilinear equation, energy integral, massive sets
Mots-clés : Liouville type theorem.

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