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Journal of Function Spaces
Volume 2015, Article ID 610858, 4 pages
http://dx.doi.org/10.1155/2015/610858
Research Article

Multiple Solutions for Kirchhoff Equations under the Partially Sublinear Case

1College of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006, China
2School of Mathematical Sciences, Shanxi University, Taiyuan 030006, China

Received 16 June 2015; Revised 12 August 2015; Accepted 26 August 2015

Academic Editor: Gennaro Infante

Copyright © 2015 Wenjun Feng and Xiaojing Feng. 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. K. Perera and Z. Zhang, “Nontrivial solutions of Kirchhoff-type problems via the Yang index,” Journal of Differential Equations, vol. 221, no. 1, pp. 246–255, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  2. B. Cheng and X. Wu, “Existence results of positive solutions of Kirchhoff type problems,” Nonlinear Analysis: Theory, Methods & Applications, vol. 71, no. 10, pp. 4883–4892, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. T. F. Ma and J. E. M. Rivera, “Positive solutions for a nonlinear nonlocal elliptic transmission problem,” Applied Mathematics Letters, vol. 16, no. 2, pp. 243–248, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. X. He and W. Zou, “Infinitely many positive solutions for Kirchhoff-type problems,” Nonlinear Analysis: Theory, Methods & Applications, vol. 70, no. 3, pp. 1407–1414, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. A. Mao and S. Luan, “Sign-changing solutions of a class of nonlocal quasilinear elliptic boundary value problems,” Journal of Mathematical Analysis and Applications, vol. 383, no. 1, pp. 239–243, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  6. J.-J. Sun and C.-L. Tang, “Existence and multiplicity of solutions for Kirchhoff type equations,” Nonlinear Analysis: Theory, Methods & Applications, vol. 74, no. 4, pp. 1212–1222, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. J. Sun and S. Liu, “Nontrivial solutions of Kirchhoff type problems,” Applied Mathematics Letters, vol. 25, no. 3, pp. 500–504, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. X. Wu, “Existence of nontrivial solutions and high energy solutions for Schrödinger-Kirchhoff-type equations in RN,” Nonlinear Analysis: Real World Applications, vol. 12, no. 2, pp. 1278–1287, 2011. View at Publisher · View at Google Scholar
  9. C. O. Alves and G. M. Figueiredo, “Nonlinear perturbations of a periodic Kirchhoff equation in RN,” Nonlinear Analysis: Theory, Methods & Applications, vol. 75, no. 5, pp. 2750–2759, 2012. View at Publisher · View at Google Scholar
  10. W. Liu and X. He, “Multiplicity of high energy solutions for superlinear Kirchhoff equations,” Journal of Applied Mathematics and Computing, vol. 39, no. 1-2, pp. 473–487, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. Y. Li, F. Li, and J. Shi, “Existence of a positive solution to Kirchhoff type problems without compactness conditions,” Journal of Differential Equations, vol. 253, no. 7, pp. 2285–2294, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. J. Jin and X. Wu, “Infinitely many radial solutions for Kirchhoff-type problems in RN,” Journal of Mathematical Analysis and Applications, vol. 369, no. 2, pp. 564–574, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. Z. Liu and Z. Wang, “On Clark's theorem and its applications to partially sublinear problems,” Annales de l'Institut Henri Poincare (C) Non Linear Analysis, 2014. View at Publisher · View at Google Scholar
  14. M. Willem, Minimax Theorems, Birkhäuser, 1996. View at Publisher · View at Google Scholar · View at MathSciNet