Abstract and Applied Analysis 
Volume 7 (2002), Issue 3, Pages 125-133
doi:10.1155/S1085337502000805

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

Abstract

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.