About this Journal Submit a Manuscript Table of Contents
International Journal of Differential Equations
Volume 2010 (2010), Article ID 673526, 12 pages
http://dx.doi.org/10.1155/2010/673526
Research Article

Multiple Solutions of Quasilinear Elliptic Equations in 𝑁

Department of Natural Sciences, Center for General Education, Chang Gung University, Taoyuan 333, Taiwan

Received 1 October 2009; Revised 15 January 2010; Accepted 1 March 2010

Academic Editor: Martin D. Schechter

Copyright © 2010 Huei-li Lin. 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. P. L. Lions, “The concentration-compactness principle in the calculus of variations. The locally compact case. I,” Annales de l'Institut Henri Poincaré. Analyse Non Linéaire, vol. 1, pp. 109–145, 1984.
  2. P. L. Lions, “The concentration-compactness principle in the calculus of variations. The locally compact case. II,” Annales de l'Institut Henri Poincaré. Analyse Non Linéaire, vol. 1, pp. 223–283, 1984.
  3. V. Benci and G. Cerami, “Positive solutions of some nonlinear elliptic problems in exterior domains,” Archive for Rational Mechanics and Analysis, vol. 99, no. 4, pp. 283–300, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. A. Bahri and Y. Y. Li, “On a min-max procedure for the existence of a positive solution for certain scalar field equations in N,” Revista Matemática Iberoamericana, vol. 6, no. 1-2, pp. 1–15, 1990. View at Zentralblatt MATH · View at MathSciNet
  5. D. M. Cao, “Multiple solutions for a Neumann problem in an exterior domain,” Communications in Partial Differential Equations, vol. 18, no. 3-4, pp. 687–700, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. G. Cerami, S. Solimini, and M. Struwe, “Some existence results for superlinear elliptic boundary value problems involving critical exponents,” Journal of Functional Analysis, vol. 69, no. 3, pp. 289–306, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. M. Struwe, Variational Methods, Springer, Berlin, Germany, 2nd edition, 1996. View at MathSciNet
  8. C. O. Alves, “Existence of positive solutions for a problem with lack of compactness involving the p-Laplacian,” Nonlinear Analysis: Theory, Methods & Applications, vol. 51, no. 7, pp. 1187–1206, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  9. G. B. Li and S. S. Yan, “Eigenvalue problems for quasilinear elliptic equations on N,” Communications in Partial Differential Equations, vol. 14, no. 8-9, pp. 1291–1314, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. J. Marcos do Ó, “On existence and concentration of positive bound states of p-Laplacian equations in N involving critical growth,” Nonlinear Analysis: Theory, Methods & Applications, vol. 62, no. 5, pp. 777–801, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  11. J. Serrin and M. Tang, “Uniqueness of ground states for quasilinear elliptic equations,” Indiana University Mathematics Journal, vol. 49, no. 3, pp. 897–923, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. Y. Li and C. Zhao, “A note on exponential decay properties of ground states for quasilinear elliptic equations,” Proceedings of the American Mathematical Society, vol. 133, no. 7, pp. 2005–2012, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. X. P. Zhu, “Multiple entire solutions of a semilinear elliptic equation,” Nonlinear Analysis: Theory, Methods & Applications, vol. 12, no. 11, pp. 1297–1316, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. C. Miranda, “Un'osservazione su un teorema di Brouwer,” Bollettino dell'Unione Matematica Italiana, vol. 3, pp. 5–7, 1940. View at Zentralblatt MATH · View at MathSciNet
  15. T.-S. Hsu, “Multiple solutions for semilinear elliptic equations in unbounded cylinder domains,” Proceedings of the Royal Society of Edinburgh A, vol. 134, no. 4, pp. 719–731, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. J. F. Yang, “Positive solutions of quasilinear elliptic obstacle problems with critical exponents,” Nonlinear Analysis: Theory, Methods & Applications, vol. 25, no. 12, pp. 1283–1306, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet