Geodesic
Some Liouville-type theorems for the stationary Ginsburg–Landau equation on quasi-model Riemannian manifolds
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 15 (2015) no. 2, pp. 127-135 
S. S. Vikharev. Some Liouville-type theorems for the stationary Ginsburg–Landau equation on quasi-model Riemannian manifolds. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 15 (2015) no. 2, pp. 127-135. http://geodesic.mathdoc.fr/item/ISU_2015_15_2_a0/
@article{ISU_2015_15_2_a0,
     author = {S. S. Vikharev},
     title = {Some {Liouville-type} theorems for the stationary {Ginsburg{\textendash}Landau} equation on quasi-model {Riemannian} manifolds},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {127--135},
     year = {2015},
     volume = {15},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2015_15_2_a0/}
}
TY  - JOUR
AU  - S. S. Vikharev
TI  - Some Liouville-type theorems for the stationary Ginsburg–Landau equation on quasi-model Riemannian manifolds
JO  - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
PY  - 2015
SP  - 127
EP  - 135
VL  - 15
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/ISU_2015_15_2_a0/
LA  - ru
ID  - ISU_2015_15_2_a0
ER  - 
%0 Journal Article
%A S. S. Vikharev
%T Some Liouville-type theorems for the stationary Ginsburg–Landau equation on quasi-model Riemannian manifolds
%J Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
%D 2015
%P 127-135
%V 15
%N 2
%U http://geodesic.mathdoc.fr/item/ISU_2015_15_2_a0/
%G ru
%F ISU_2015_15_2_a0

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we find the conditions for validity of Liouville-type theorems for bounded solutions of the stationary Ginsburg–Landau equation and quasilinear elliptic inequality $-\Delta u \geqslant u^q$, $q>1$, on quasi-model Riemannian manifolds.

[1] Losev A. G., “Certain Liouville Theorems for Riemannian Manifolds of a Special Form”, Soviet Math., 35:12 (1991), 15–23 | MR | Zbl

[2] Losev A. G., “On some Liouville theorems on noncompact Riemannian manifolds”, Siberian Math. J., 39:1 (1998), 74–80 | DOI | MR | Zbl

[3] Losev A. G., Mazepa E. A., “Bounded solutions of the Schrodinger equation on Riemannian products”, St. Petersburg Math. J., 13:1 (2002), 57–73 | MR | Zbl

[4] Losev A. G., Fedorenko Iu. S., “Positive solutions of quasilinear elliptic inequalities on noncompact Riemannian manifolds”, Math. Notes, 81:6 (2007), 778–787 | DOI | DOI | MR | Zbl

[5] Losev A. G., Mazepa E. A., “On Asymptotical Behavior of the Positive Solutions Some Quasilinear Inequalities on Model Riemannian Manifolds”, Science Journal of VolSU. Mathematics. Physics, 2013, no. 1(18), 59–69 (in Russian) | MR

[6] Bidaut-Veron M., Pohozaev S. I., “Non-existence results and estimates for some nonlinear elliptic problems”, J. Anal. Math., 84 (2001), 1–49 | DOI | MR | Zbl

[7] Diaz J. I., Nonlinear Partial Differential Equations and Free Boundary Problem, v. 1, Pitman Research Notes in Mathematics, 106, Elliptic Equations, Pitman, Boston, 1985, 323 pp. | DOI | MR

[8] Dancer E. N., Du Y., “Some remarks on Liouville type results for quasilinear elliptic equations”, Proc. Amer. Math. Soc., 131:6 (2002), 1891–1899 | DOI | MR

[9] Pigola S., Rigoli M., Setti A. G., “A Liouville-type result for quasi-linear elliptic equations on complete Riemannian manifolds”, J. Functional Analysis, 219:2 (2005), 400–432 | DOI | MR | Zbl

[10] Grigor'yan A., “Analytic and geometric background of recurrence and non-explosion of the Browman motion on Riemannian manifolds”, Bull. Amer. Math. Soc., 36 (1999), 135–249 | DOI | MR | Zbl

[11] Serrin J., Zou H., “Cauchy–Liouville and universal boundedness theorems for quasilinear elliptic equations and inequalities”, Acta. Math., 189 (2002), 79–142 | DOI | MR | Zbl

[12] Ginzburg V. L., Landau L. D., “On the theory of superconductivity”, Journal of Experimental and Theoretical Physics, 20 (1950), 1064–1091 (in Russian)

[13] Aranson I. S., Kramer L., “The world of the complex Ginzburg–Landau equation”, Rev. Mod. Phys., 74:1 (2002), 99–143 | DOI | MR | Zbl

[14] Aronson D. G., Weinberger H. F., “Multidimensional nonlinear diffusion arising in population genetics”, Advances in Math., 30 (1978), 33–76 | DOI | MR | Zbl

[15] Tolksdorf P., “Regularity for more general class of quasilinear elliptic equations”, J. Differ. Equations, 51 (1984), 126–150 | DOI | MR | Zbl