THE EXISTENCE AND NON-EXISTENCE OF SIGN-CHANGING SOLUTIONS TO BI-HARMONIC EQUATIONS WITH A p-LAPLACIAN

We investigate the bi-harmonic problem{Δ^(2)u-α▽·(f(▽u))-βΔ_(p)u=g(x,u) in Ω,δu/δn=0,δ(Δu)/δn=0 on δΩ,where Δ^(2)u=Δ(Δu),Δ_(p)u=div(|▽u|^(p-2)▽u)with p>2.Ω is a bounded smooth domain in R^(N),N≥1.By using a special function space with the constraint ∫_(Ω)udx=0,under suitable assumptions on f and g(x,u),we show the existence and multiplicity of sign-changing solutions to the above problem via the Mountain pass theorem and the Fountain theorem.Recent results from the literature are extended.