Table of Contents Author Guidelines Submit a Manuscript
International Journal of Differential Equations
Volume 2010 (2010), Article ID 984671, 23 pages
http://dx.doi.org/10.1155/2010/984671
Research Article

The Second Eigenvalue of the -Laplacian as Goes to

Mathematisches Institut, Universität zu Köln, Weyertal 86-90, D 50931 Köln , Germany

Received 15 July 2009; Accepted 29 September 2009

Academic Editor: Norimichi Hirano

Copyright © 2010 Enea Parini. 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.

Citations to this Article [10 citations]

The following is the list of published articles that have cited the current article.

  • Enea Parini, “Continuity of the variational eigenvalues of the p-Laplacian with respect to p,” Bulletin of the Australian Mathematical Society, vol. 83, no. 3, pp. 376–381, 2011. View at Publisher · View at Google Scholar
  • Lorenzo Brasco, and Giovanni Franzina, “On the Hong–Krahn–Szego inequality for the p-Laplace operator,” Manuscripta Mathematica, 2012. View at Publisher · View at Google Scholar
  • Zoja Milbers, and Friedemann Schuricht, “Necessary condition for eigensolutions of the 1-Laplace operator by means of inner variations,” Mathematische Annalen, vol. 356, no. 1, pp. 147–177, 2012. View at Publisher · View at Google Scholar
  • Jií Benedikt, Pavel Drábek, and Petr Girg, “The second eigenfunction of the p-Laplacian on the disk is not radial,” Nonlinear Analysis, Theory, Methods and Applications, vol. 75, no. 12, pp. 4422–4435, 2012. View at Publisher · View at Google Scholar
  • Samuel Littig, and Friedemann Schuricht, “Convergence of the eigenvalues of the $$p$$ -Laplace operator as $$p$$ goes to 1,” Calculus of Variations and Partial Differential Equations, 2013. View at Publisher · View at Google Scholar
  • Barbara Brandolini, Francesco Della Pietra, Carlo Nitsch, and Cristina Trombetti, “Symmetry breaking in a constrained Cheeger type isoperimetric inequality,” ESAIM: Control, Optimisation and Calculus of Variations, 2014. View at Publisher · View at Google Scholar
  • Vladimir Bobkov, and Pavel Drábek, “On some unexpected properties of radial and symmetric eigenvalues and eigenfunctions of the p-Laplacian on a disk,” Journal of Differential Equations, vol. 263, no. 3, pp. 1755–1772, 2016. View at Publisher · View at Google Scholar
  • Anoop, Drábek, and Sarath Sasi, “On the structure of the second eigenfunctions of the p-laplacian on a ball,” Proceedings of the American Mathematical Society, vol. 144, no. 6, pp. 2503–2512, 2016. View at Publisher · View at Google Scholar
  • Bernd Kawohl, and Jiří Horák, “On the geometry of the p-Laplacian operator,” Discrete and Continuous Dynamical Systems - Series S, vol. 10, no. 4, pp. 799–813, 2017. View at Publisher · View at Google Scholar
  • M. Caroccia, “Cheeger N-clusters,” Calculus of Variations and Partial Differential Equations, vol. 56, no. 2, 2017. View at Publisher · View at Google Scholar