Abstract and Applied Analysis
Volume 7 (2002), Issue 3, Pages 125-133

On the existence of solutions to a fourth-order quasilinear resonant problem

Shibo Liu1 and Marco Squassina2

1Institute of Mathematics, Academy of Mathematics and Systems Sciences, Academia Sinica, Beijing 100080, China
2Dipartimento di Matematica, Università Cattolica S.C., Via Musei 41, Brescia 25121, Italy

Received 7 November 2001

Copyright © 2002 Shibo Liu and Marco Squassina. 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.


By means of Morse theory we prove the existence of a nontrivial solution to a superlinear p-harmonic elliptic problem with Navier boundary conditions having a linking structure around the origin. Moreover, in case of both resonance near zero and nonresonance at + the existence of two nontrivial solutions is shown.