Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2012, Article ID 760854, 44 pages
Research Article

Dirichlet and Neumann Problems Related to Nonlinear Elliptic Systems: Solvability, Multiple Solutions, Solutions with Positive Components

Department of Mathematics and Applications, “R. Caccioppoli.,” University of Naples “Federico II”, Via Claudio 21, 80125 Naples, Italy

Received 1 February 2012; Accepted 2 April 2012

Academic Editor: D. O'Regan

Copyright © 2012 Luisa Toscano and Speranza Toscano. 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. Toscano and S. Toscano, “On the solvability of a class of general systems of variational equations with nonmonotone operators,” Journal of Interdisciplinary Mathematics, vol. 14, no. 2, pp. 123–147, 2011. View at Google Scholar · View at Zentralblatt MATH
  2. P. Drábek and S. I. Pohozaev, “Positive solutions for the p-Laplacian: application of the fibering method,” Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, vol. 127, no. 4, pp. 703–726, 1997. View at Publisher · View at Google Scholar
  3. S. I. Pohozaev and L. Véron, “Multiple positive solutions of some quasilinear Neumann problems,” Applicable Analysis, vol. 74, no. 3-4, pp. 363–390, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. A. Anane, “Simplicité et isolation de la première valeur propre du p-laplacien avec poids,” Comptes Rendus des Séances de l'Académie des Sciences. Série I. Mathématique, vol. 305, no. 16, pp. 725–728, 1987. View at Google Scholar
  5. P. Tolksdorf, “Regularity for a more general class of quasilinear elliptic equations,” Journal of Differential Equations, vol. 51, no. 1, pp. 126–150, 1984. View at Publisher · View at Google Scholar
  6. N. S. Trudinger, “On Harnack type inequalities and their application to quasilinear elliptic equations,” Communications on Pure and Applied Mathematics, vol. 20, pp. 721–747, 1967. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. P. Drabek, Strongly Nonlinear Degenerated and Singular Elliptic Problems, vol. 343 of Pitman Research Notes in Math, Longman, London, UK, 1996.