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

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 $+\infty$ the existence of two nontrivial solutions is shown.