A Liouville-type theorem for the p-laplacian with potential term
Pinchover, Yehuda ; Tertikas, Achilles ; Tintarev, Kyril
Annales de l'I.H.P. Analyse non linéaire, Tome 25 (2008), p. 357-368 / Harvested from Numdam
@article{AIHPC_2008__25_2_357_0,
     author = {Pinchover, Yehuda and Tertikas, Achilles and Tintarev, Kyril},
     title = {A Liouville-type theorem for the $p$-laplacian with potential term},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {25},
     year = {2008},
     pages = {357-368},
     doi = {10.1016/j.anihpc.2006.12.004},
     zbl = {1151.35027},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2008__25_2_357_0}
}
Pinchover, Yehuda; Tertikas, Achilles; Tintarev, Kyril. A Liouville-type theorem for the $p$-laplacian with potential term. Annales de l'I.H.P. Analyse non linéaire, Tome 25 (2008) pp. 357-368. doi : 10.1016/j.anihpc.2006.12.004. http://gdmltest.u-ga.fr/item/AIHPC_2008__25_2_357_0/

[1] Agmon S., Bounds on exponential decay of eigenfunctions of Schrödinger operators, in: Schrödinger Operators, Como, 1984, Lecture Notes in Math., vol. 159, Springer, Berlin, 1985, pp. 1-38. | MR 824986 | Zbl 0583.35027

[2] Allegretto W., Huang Y.X., A Picone's identity for the p-Laplacian and applications, Nonlinear Anal. 32 (1998) 819-830. | MR 1618334 | Zbl 0930.35053

[3] Allegretto W., Huang Y.X., Principal eigenvalues and Sturm comparison via Picone's identity, J. Differential Equations 156 (1999) 427-438. | MR 1705379 | Zbl 0937.35117

[4] Barbatis G., Filippas S., Tertikas A., A unified approach to improved L p Hardy inequalities with best constants, Trans. Amer. Math. Soc. 356 (2004) 2169-2196. | MR 2048514 | Zbl 1129.26019

[5] Diaz J.I., Saá J.E., Existence et unicité de solutions positives pour certaines équations elliptiques quasilinéaires, C. R. Acad. Sci. Paris Ser. I Math. 305 (1987) 521-524. | MR 916325 | Zbl 0656.35039

[6] Heinonen J., Kilpeläinen T., Martio O., Nonlinear Potential Theory of Degenerate Elliptic Equations, Oxford Mathematical Monographs, Oxford University Press, New York, 1993. | MR 1207810 | Zbl 0780.31001

[7] Mitidieri A., Pokhozhaev S.I., Some generalizations of Bernstein's theorem, Differ. Uravn. 38 (2002) 373-378, Translation in Differ. Equ. 38 (2002) 392-397. | MR 2005075 | Zbl pre01916050

[8] Murata M., Structure of positive solutions to (-Δ+V)u=0 in R n , Duke Math. J. 53 (1986) 869-943. | MR 874676 | Zbl 0624.35023

[9] Pinchover Y., A Liouville-type theorem for Schrödinger operators, Comm. Math. Phys. 272 (2007) 75-84. | MR 2291802 | Zbl 1135.35021

[10] Pinchover Y., Tintarev K., Ground state alternative for p-Laplacian with potential term, Calc. Var. Partial Differential Equations 28 (2007) 179-201. | MR 2284565 | Zbl pre05116487

[11] Poliakovsky A., Shafrir I., Uniqueness of positive solutions for singular problems involving the p-Laplacian, Proc. Amer. Math. Soc. 133 (2005) 2549-2557. | MR 2146198 | Zbl 1086.35051

[12] Serrin J., Local behavior of solutions of quasi-linear equations, Acta Math. 111 (1964) 247-302. | MR 170096 | Zbl 0128.09101

[13] Serrin J., Isolated singularities of solutions of quasi-linear equations, Acta Math. 113 (1965) 219-240. | MR 176219 | Zbl 0173.39202

[14] Shafrir I., Asymptotic behaviour of minimizing sequences for Hardy's inequality, Commun. Contemp. Math. 2 (2000) 151-189. | MR 1759788 | Zbl 0956.35036

[15] Tolksdorf P., Regularity for a more general class of quasilinear elliptic equations, J. Differential Equations 51 (1984) 126-150. | MR 727034 | Zbl 0488.35017