International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 45-48, Pages 2453-2472
doi:10.1155/S0161171204305119

Multiple solutions to a nonlinear elliptic equation involving Paneitz type operators

Abstract

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.