Mazepa E.A. On asymptotical behavior of the solutions some semilinear elliptical equations on noncompact riemannian manifolds

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Mazepa Elena Alexeevna

Candidate of Physics and Mathematics, Associate Professor, Chair of Fundamental Information Science and Optimal Control, Volgograd State University
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Prosp. Universitetsky, 100, 400062 Volgograd, Russian Federation

Abstract. This paper is devoted to studying the asymptotical behavior of the solutions of some semilinear equations on noncompact Riemannian manifolds. We establish some interrelation between validity of the Liouville property for linear elliptical equations with constant positive potential and validity of the Liouville theorem for one semilinear elliptic equation on these manifolds. Also we receive the necessary and sufficient conditions of existence of the nontrivial (positive) bounded entire solutions of the semilinear elliptic equations and solvability of some boundary value problems on the quasi-model Riemannian manifolds.

Key words: semilinear elliptic equation, Liouville property, boundary value problem, Riemannian manifold, Dirichlet problem.

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On asymptotical behavior of the solutions some semilinear elliptical equations on noncompact Riemannian manifolds by Mazepa E.A. is licensed under a Creative Commons Attribution 4.0 International License.

Citation in English: Science Journal of Volgograd State University. Mathematics. Physics. №1 (14) 2011 pp. 41-59

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