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Matematicheskie Zametki, 2007, Volume 81, Issue 6, Pages 867–878
DOI: https://doi.org/10.4213/mzm3737
(Mi mzm3737)
 

This article is cited in 8 scientific papers (total in 9 papers)

Positive Solutions of Quasilinear Elliptic Inequalities on Noncompact Riemannian Manifolds

A. G. Losev, Yu. S. Fedorenko

Volgograd State University
Full-text PDF (467 kB) Citations (9)
References:
Abstract: In this paper, we consider the generalized solutions of the inequality
div(A(x,u,u)u)F(x,u,u)uq,q>1,
on noncompact Riemannian manifolds. We obtain sufficient conditions for the validity of Liouville's theorem on the triviality of the positive solutions of the inequality under consideration. We also obtain sharp conditions for the existence of a positive solution of the inequality Δuuq, q>1, on spherically symmetric noncompact Riemannian manifolds.
Keywords: quasilinear elliptic inequality, Riemannian manifold, theorem of Liouville type, Lipschitz function, quasisimilar manifold, Laplace–Beltrami operator.
Received: 22.12.2005
English version:
Mathematical Notes, 2007, Volume 81, Issue 6, Pages 778–787
DOI: https://doi.org/10.1134/S0001434607050252
Bibliographic databases:
UDC: 517.95
Language: Russian
Citation: A. G. Losev, Yu. S. Fedorenko, “Positive Solutions of Quasilinear Elliptic Inequalities on Noncompact Riemannian Manifolds”, Mat. Zametki, 81:6 (2007), 867–878; Math. Notes, 81:6 (2007), 778–787
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/mzm3737
  • https://doi.org/10.4213/mzm3737
  • https://www.mathnet.ru/eng/mzm/v81/i6/p867
    Erratum
    This publication is cited in the following 9 articles:
    1. S. S. Vikharev, A. G. Losev, “Triviality of Bounded Solutions of the Stationary Ginzburg–Landau Equation on Spherically Symmetric Manifolds”, Math. Notes, 101:2 (2017), 208–218  mathnet  crossref  crossref  mathscinet  isi  elib
    2. Losev A.G., “Solvability of the Dirichlet Problem For the Poisson Equation on Some Noncompact Riemannian Manifolds”, Differ. Equ., 53:12 (2017), 1595–1604  crossref  mathscinet  zmath  isi  scopus
    3. S. S. Vikharev, “O nekotorykh liuvillevykh teoremakh dlya statsionarnogo uravneniya Ginzburga–Landau na kvazimodelnykh rimanovykh mnogoobraziyakh”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 15:2 (2015), 127–135  mathnet  crossref  elib
    4. E. A. Mazepa, “The positive solutions to quasilinear elliptic inequalities on model Riemannian manifolds”, Russian Math. (Iz. VUZ), 59:9 (2015), 18–25  mathnet  crossref
    5. A. P. Sazonov, “Polozhitelnye resheniya ellipticheskikh uravnenii na rimanovykh mnogoobraziyakh spetsialnogo vida”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2015, no. 3(28), 6–18  mathnet  crossref
    6. E. A. Mazepa, “Polozhitelnye resheniya kvazilineinykh ellipticheskikh neravenstv na rimanovykh proizvedeniyakh”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2015, no. 6(31), 6–16  mathnet  crossref
    7. A. G. Losev, E. A. Mazepa, “On asymptotic behavior of positive solutions of some quasilinear inequalities on model Riemannian manifolds”, Ufa Math. J., 5:1 (2013), 83–89  mathnet  crossref  mathscinet  isi  elib
    8. Losev A.G., Sazonov A.P., “Ob asimptoticheskom povedenii reshenii nekotorykh polulineinykh uravnenii na modelnykh rimanovykh mnogoobraziyakh”, Vestnik Volgogradskogo gosudarstvennogo universiteta. Seriya 1: Matematika. Fizika, 2013, no. 2(219), 36–56  elib
    9. A. G. Losev, Yu. S. Fedorenko, “Letter to the Editor”, Math. Notes, 85:3 (2009), 463–463  mathnet  crossref  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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