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The liouville property and boundary value problems for semilinear elliptic equations on noncompact Riemannian manifolds

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Abstract

We address the asymptotic behavior of solutions to semilinear equations on noncompact Riemannian manifolds. Under study is the relation between the solvability of some boundary and exterior boundary value problems as well as conditions for the fulfillment and stability of Liouville-type theorems for the solutions to semilinear equations on these manifolds.

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Authors and Affiliations

  1. Volgograd State University, Volgograd, Russia

    E. A. Mazepa

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  1. E. A. Mazepa
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Correspondence to E. A. Mazepa.

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Original Russian Text Copyright © 2012 Mazepa E. A.

The author was supported by the Russian Foundation for Basic Research (Grant 10-01-97004-p povolzh’e_a).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 53, No. 1, pp. 165–179, January–February, 2012.

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Mazepa, E.A. The liouville property and boundary value problems for semilinear elliptic equations on noncompact Riemannian manifolds. Sib Math J 53, 134–145 (2012). https://doi.org/10.1134/S0037446612010119

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  • DOI: https://doi.org/10.1134/S0037446612010119

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