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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 275748, 9 pages
http://dx.doi.org/10.1155/2012/275748
Research Article

Existence and Nonexistence of Positive Solutions for Quasilinear Elliptic Problem

Institut Supérieur d'Informatique et de Multimédia de Gabè (ISIMG), Campus Universitaire Cité Erriadh, Zirig-Gabes 6075, Tunisia

Received 18 April 2012; Accepted 21 June 2012

Academic Editor: Sergey Piskarev

Copyright © 2012 K. Saoudi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. V. Rădulescu and D. Repovš, “Combined effects in nonlinear problems arising in the study of anisotropic continuous media,” Nonlinear Analysis, vol. 75, no. 3, pp. 1524–1530, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. C. A. Santos, “Non-existence and existence of entire solutions for a quasi-linear problem with singular and super-linear terms,” Nonlinear Analysis, vol. 72, no. 9-10, pp. 3813–3819, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. M. Cuesta and P. Takáč, “A strong comparison principle for positive solutions of degenerate elliptic equations,” Differential and Integral Equations, vol. 13, no. 4–6, pp. 721–746, 2000. View at Zentralblatt MATH
  4. P. Lindqvist, “On the equation div(|u|p-2u)+λ|u|p-2u=0,” Proceedings of the American Mathematical Society, vol. 109, no. 1, pp. 157–164, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. A. Anane, “Simplicité et isolation de la première valeur propre du p-laplacien avec poids,” Comptes Rendus des Séances de l'Académie des Sciences I, vol. 305, no. 16, pp. 725–728, 1987.
  6. R. Filippucci, P. Pucci, and V. Rădulescu, “Existence and non-existence results for quasilinear elliptic exterior problems with nonlinear boundary conditions,” Communications in Partial Differential Equations, vol. 33, no. 4–6, pp. 706–717, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. P. Pucci and R. Servadei, “Regularity of weak solutions of homogeneous or inhomogeneous quasilinear elliptic equations,” Indiana University Mathematics Journal, vol. 57, no. 7, pp. 3329–3363, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. E. DiBenedetto, “C1+α local regularity of weak solutions of degenerate elliptic equations,” Nonlinear Analysis, vol. 7, no. 8, pp. 827–850, 1983. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. P. Pucci and J. Serrin, “Maximum principles for elliptic partial differential equations,” in Handbook of Differential Equations: Stationary Partial Differential Equations, M. Chipot, Ed., vol. 4, pp. 355–483, Elsevier, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH