International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 46, Pages 2453-2472

Multiple solutions to a nonlinear elliptic equation involving Paneitz type operators

Abdallah El Hamidi

Laboratoire de Mathématiques et Applications, Université de La Rochelle, avenue Michel Crépeau, La Rochelle 17000, France

Received 12 May 2003

Copyright © 2004 Abdallah El Hamidi. 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.


This paper deals with an elliptic equation involving Paneitz type operators on compact Riemannian manifolds with concave-convex nonlinearities and a real parameter. Nonlocal and multiple existence results are established. Characteristic values of the real parameter are introduced and their role in the change of the energy sign and the existence of positive solutions are highlighted.