A Liouville-type theorem for the p-laplacian with potential term

Yehuda Pinchover; Achilles Tertikas; Kyril Tintarev

Annales de l'I.H.P. Analyse non linéaire (2008)

  • Volume: 25, Issue: 2, page 357-368
  • ISSN: 0294-1449

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Pinchover, Yehuda, Tertikas, Achilles, and Tintarev, Kyril. "A Liouville-type theorem for the p-laplacian with potential term." Annales de l'I.H.P. Analyse non linéaire 25.2 (2008): 357-368. <http://eudml.org/doc/78793>.

@article{Pinchover2008,
author = {Pinchover, Yehuda, Tertikas, Achilles, Tintarev, Kyril},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {-Laplacian; ground state; Liouville comparison principle; positive solution},
language = {eng},
number = {2},
pages = {357-368},
publisher = {Elsevier},
title = {A Liouville-type theorem for the p-laplacian with potential term},
url = {http://eudml.org/doc/78793},
volume = {25},
year = {2008},
}

TY - JOUR
AU - Pinchover, Yehuda
AU - Tertikas, Achilles
AU - Tintarev, Kyril
TI - A Liouville-type theorem for the p-laplacian with potential term
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2008
PB - Elsevier
VL - 25
IS - 2
SP - 357
EP - 368
LA - eng
KW - -Laplacian; ground state; Liouville comparison principle; positive solution
UR - http://eudml.org/doc/78793
ER -

References

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  2. [2] Allegretto W., Huang Y.X., A Picone's identity for the p-Laplacian and applications, Nonlinear Anal.32 (1998) 819-830. Zbl0930.35053MR1618334
  3. [3] Allegretto W., Huang Y.X., Principal eigenvalues and Sturm comparison via Picone's identity, J. Differential Equations156 (1999) 427-438. Zbl0937.35117MR1705379
  4. [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. Zbl1129.26019MR2048514
  5. [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. Zbl0656.35039MR916325
  6. [6] Heinonen J., Kilpeläinen T., Martio O., Nonlinear Potential Theory of Degenerate Elliptic Equations, Oxford Mathematical Monographs, Oxford University Press, New York, 1993. Zbl0780.31001MR1207810
  7. [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. Zbl1274.35120MR2005075
  8. [8] Murata M., Structure of positive solutions to ( - Δ + V ) u = 0 in R n , Duke Math. J.53 (1986) 869-943. Zbl0624.35023MR874676
  9. [9] Pinchover Y., A Liouville-type theorem for Schrödinger operators, Comm. Math. Phys.272 (2007) 75-84. Zbl1135.35021MR2291802
  10. [10] Pinchover Y., Tintarev K., Ground state alternative for p-Laplacian with potential term, Calc. Var. Partial Differential Equations28 (2007) 179-201. Zbl1208.35032MR2284565
  11. [11] Poliakovsky A., Shafrir I., Uniqueness of positive solutions for singular problems involving the p-Laplacian, Proc. Amer. Math. Soc.133 (2005) 2549-2557. Zbl1086.35051MR2146198
  12. [12] Serrin J., Local behavior of solutions of quasi-linear equations, Acta Math.111 (1964) 247-302. Zbl0128.09101MR170096
  13. [13] Serrin J., Isolated singularities of solutions of quasi-linear equations, Acta Math.113 (1965) 219-240. Zbl0173.39202MR176219
  14. [14] Shafrir I., Asymptotic behaviour of minimizing sequences for Hardy's inequality, Commun. Contemp. Math.2 (2000) 151-189. Zbl0956.35036MR1759788
  15. [15] Tolksdorf P., Regularity for a more general class of quasilinear elliptic equations, J. Differential Equations51 (1984) 126-150. Zbl0488.35017MR727034

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