Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2006, Article ID 95480, 18 pages
http://dx.doi.org/10.1155/AAA/2006/95480

Existence of positive solutions for nonlinear boundary value problems in bounded domains of n

Département de Mathématiques, Faculté des Sciences de Tunis, Campus Universitaire, Tunis 2092, Tunisia

Received 10 June 2004; Accepted 22 September 2004

Copyright © 2006 Faten Toumi. 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. M. Aizenman and B. Simon, “Brownian motion and Harnack inequality for Schrödinger operators,” Communications on Pure and Applied Mathematics, vol. 35, no. 2, pp. 209–273, 1982. View at Publisher · View at Google Scholar
  2. S. Athreya, “On a singular semilinear elliptic boundary value problem and the boundary Harnack principle,” Potential Analysis. An International Journal Devoted to the Interactions between Potential Theory, Probability Theory, Geometry and Functional Analysis, vol. 17, no. 3, pp. 293–301, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. H. Brezis and S. Kamin, “Sublinear elliptic equations in Rn,” Manuscripta Mathematica, vol. 74, no. 1, pp. 87–106, 1992. View at Publisher · View at Google Scholar
  4. K. L. Chung and Z. X. Zhao, From Brownian Motion to Schrödinger's Equation, vol. 312 of Grundlehren der Mathematischen Wissenschaften, Springer, Berlin, 1995.
  5. R. Dalmasso, “Existence and uniqueness results for polyharmonic equations,” Nonlinear Analysis. Theory, Methods & Applications. An International Multidisciplinary Journal. Series A: Theory and Methods, vol. 36, no. 1, pp. 131–137, 1999. View at Google Scholar
  6. R. Dautray and J.-L. Lions, Analyse mathématique et calcul numérique pour les sciences et les techniques. Vol. 1, L'oprateur de Laplace, INSTN: Collection Enseignement. [INSTN: Teaching Collection], Masson, Paris, 1987.
  7. N. J. Kalton and I. E. Verbitsky, “Nonlinear equations and weighted norm inequalities,” Transactions of the American Mathematical Society, vol. 351, no. 9, pp. 3441–3497, 1999. View at Publisher · View at Google Scholar
  8. H. Mâagli, “Inequalities for the Riesz potentials,” Archives of Inequalities and Applications. An International Journal for Theory and Applications, vol. 1, no. 3-4, pp. 285–294, 2003. View at Google Scholar
  9. H. Mâagli and L. Mâatoug, “Singular solutions of a nonlinear equation in bounded domains of R2,” Journal of Mathematical Analysis and Applications, vol. 270, no. 1, pp. 230–246, 2002. View at Google Scholar
  10. H. Mâagli and M. Zribi, “On a new Kato class and singular solutions of a nonlinear elliptic equation in bounded domains of n,” to appear in Positivity.
  11. S. C. Port and C. J. Stone, Brownian motion and classical potential theory, Probability and Mathematical Statistics, Academic Press, New York, 1978.
  12. M. Selmi, “Inequalities for Green functions in a Dini-Jordan domain in R2,” Potential Analysis. An International Journal Devoted to the Interactions between Potential Theory, Probability Theory, Geometry and Functional Analysis, vol. 13, no. 1, pp. 81–102, 2000. View at Google Scholar
  13. N. Zeddini, “Positive solutions for a singular nonlinear problem on a bounded domain in 2,” Potential Analysis. An International Journal Devoted to the Interactions between Potential Theory, Probability Theory, Geometry and Functional Analysis, vol. 18, no. 2, pp. 97–118, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. Z. X. Zhao, “Uniform boundedness of conditional gauge and Schrödinger equations,” Communications in Mathematical Physics, vol. 93, no. 1, pp. 19–31, 1984. View at Publisher · View at Google Scholar