Table of Contents
International Journal of Analysis
Volume 2014, Article ID 320527, 15 pages
http://dx.doi.org/10.1155/2014/320527
Research Article

Existence and Nonexistence of a Solution for a Nonlinear -Elliptic Problem with Right-Hand Side Measure

1Laboratory LAMA, Department of Mathematics, Faculty of Sciences Dhar El Mahraz, University of Fez, Atlas, 1796 Fez, Morocco
2Faculty of Juridical, Economic and Social Sciences, Hassan 1st University, BP 539, Settat, Morocco

Received 4 November 2013; Accepted 24 February 2014; Published 4 May 2014

Academic Editor: Mats Ehrnstrom

Copyright © 2014 Elhoussine Azroul et al. 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. L. Boccardo, T. Gallouët, and L. Orsina, “Existence and nonexistence of solutions for some nonlinear elliptic equations,” Journal d'Analyse Mathématique, vol. 73, pp. 203–223, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. P. Baras and M. Pierre, “Singularités éliminables pour des équations semi-linéaires,” Annales de l'Institut Fourier, vol. 34, no. 1, pp. 185–206, 1984. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. H. Brezis, “Nonlinear elliptic equations involving measures,” in Contributions to Nonlinear Partial Differential Equations, vol. 89 of Research Notes in Mathematics, pp. 82–89, Pitman, Boston, Mass, USA, 1981. View at Google Scholar
  4. T. Gallouët and J.-M. Morel, “Resolution of a semilinear equation in L1,” Proceedings of the Royal Society of Edinburgh A. Mathematics, vol. 96, no. 3-4, pp. 275–288, 1984. View at Publisher · View at Google Scholar · View at MathSciNet
  5. X. L. Fan and D. Zhao, “On the generalised Orlicz-Sobolev Space Wk,p(x)(Ω),” Journal of Gansu Education College, vol. 12, no. 1, pp. 1–6, 1998. View at Google Scholar
  6. D. Zhao, W. J. Qiang, and X. L. Fan, “On genzralised Orlicz spaces Lp(x)(Ω),” Journal of Gansu Sciences, vol. 9, no. 2, pp. 1–7, 1997. View at Google Scholar
  7. P. Harjulehto and P. Hästö, “Sobolev inequalities with variable exponent attaining the values 1 and n,” Publicacions Matemàtiques, vol. 52, no. 2, pp. 347–363, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. L. Diening, P. Harjulehto, P. Hästö, and M. Růžička, Lebesgue and Sobolev Spaces with Variable Exponents, vol. 2017 of Lecture Notes in Mathematics, Springer, Heidelberg, Germany, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  9. M. B. Benboubker, E. Azroul, and A. Barbara, “Quasilinear elliptic problems with nonstandard growth,” Electronic Journal of Differential Equations, vol. 2011, no. 62, pp. 1–16, 2011. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. J.-L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod et Gauthiers-Villars, Paris, France, 1969. View at MathSciNet
  11. G. Stampacchia, “Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus,” Annales de l'Institut Fourier, vol. 15, pp. 189–258, 1965. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet