Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2011, Article ID 526026, 13 pages
http://dx.doi.org/10.1155/2011/526026
Research Article

Multiplicity of Solutions for Nonlocal Elliptic System of (𝑝,π‘ž)-Kirchhoff Type

1College of Mathematics and Information Science, Qujing Normal University, Qujing, Yunnan 655011, China
2Department of Mathematics, Yunnan Normal University, Kunming, Yunnan 650092, China

Received 16 May 2011; Accepted 23 June 2011

Academic Editor: Josip E. PečariΔ‡

Copyright Β© 2011 Bitao Cheng 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. G. Kirchhoff, Mechanik, Teubner, leipzig, Germany, 1883.
  2. C. O. Alves, F. J. S. A. CorrΓͺa, and T. F. Ma, β€œPositive solutions for a quasilinear elliptic equation of Kirchhoff type,” Computers & Mathematics with Applications, vol. 49, no. 1, pp. 85–93, 2005. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  3. B. Cheng and X. Wu, β€œExistence results of positive solutions of Kirchhoff type problems,” Nonlinear Analysis. Theory, Methods & Applications, vol. 71, no. 10, pp. 4883–4892, 2009. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  4. B. Cheng, X. Wu, and J. Liu, β€œMultiplicity of nontrivial solutions for Kirchhoff type problems,” Boundary Value Problems, vol. 2010, Article ID 268946, 13 pages, 2010. View at Publisher Β· View at Google Scholar
  5. M. Chipot and B. Lovat, β€œSome remarks on nonlocal elliptic and parabolic problems,” Nonlinear Analysis. Theory, Methods & Applications, vol. 30, no. 7, pp. 4619–4627, 1997. View at Publisher Β· View at Google Scholar
  6. P. D'Ancona and S. Spagnolo, β€œGlobal solvability for the degenerate Kirchhoff equation with real analytic data,” Inventiones Mathematicae, vol. 108, no. 2, pp. 247–262, 1992. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  7. X. He and W. Zou, β€œInfinitely many positive solutions for Kirchhoff-type problems,” Nonlinear Analysis. Theory, Methods & Applications, vol. 70, no. 3, pp. 1407–1414, 2009. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  8. T. Ma and J. E. MuΓ±oz Rivera, β€œPositive solutions for a nonlinear nonlocal elliptic transmission problem,” Applied Mathematics Letters, vol. 16, no. 2, pp. 243–248, 2003. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  9. T. Ma, β€œRemarks on an elliptic equation of Kirchhoff type,” Nonlinear Analysis. Theory, Methods & Applications, vol. 63, pp. 1967–1977, 2005. View at Google Scholar
  10. A. Mao and Z. Zhang, β€œSign-changing and multiple solutions of Kirchhoff type problems without the P.S. condition,” Nonlinear Analysis. Theory, Methods & Applications, vol. 70, no. 3, pp. 1275–1287, 2009. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  11. K. Perera and Z. Zhang, β€œNontrivial solutions of Kirchhoff-type problems via the Yang index,” Journal of Differential Equations, vol. 221, no. 1, pp. 246–255, 2006. View at Publisher Β· View at Google Scholar
  12. Z. Zhang and K. Perera, β€œSign changing solutions of Kirchhoff type problems via invariant sets of descent flow,” Journal of Mathematical Analysis and Applications, vol. 317, no. 2, pp. 456–463, 2006. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  13. F. J. S. A. CorrΓͺa and R. G. Nascimento, β€œOn a nonlocal elliptic system of p-Kirchhoff-type under Neumann boundary condition,” Mathematical and Computer Modelling, vol. 49, no. 3-4, pp. 598–604, 2009. View at Publisher Β· View at Google Scholar
  14. G. Bonanno, β€œMultiple critical points theorems without the Palais-Smale condition,” Journal of Mathematical Analysis and Applications, vol. 299, no. 2, pp. 600–614, 2004. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  15. G. Bonanno, β€œA minimax inequality and its applications to ordinary differential equations,” Journal of Mathematical Analysis and Applications, vol. 270, no. 1, pp. 210–229, 2002. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  16. B. Ricceri, β€œOn a three critical points theorem,” Archiv der Mathematik, vol. 75, no. 3, pp. 220–226, 2000. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  17. G. Talenti, β€œSome inequalities of Sobolev type on two-dimensional spheres,” in General Inequalities, W. Walter, Ed., vol. 5 of Internat. Schriftenreihe Numer. Math., pp. 401–408, BirkhΓ€user, Basel, Germany, 1987. View at Google Scholar Β· View at Zentralblatt MATH