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

作　　者：Wenqing WANG Anmin MAO 王文清;毛安民(Department of Mathematics,Wuhan University of Technology,Wuhan 430071,China;School of Mathematical Sciences,Qufu Normal University,Shandong 273165,China)

机构地区：[1]Department of Mathematics,Wuhan University of Technology,Wuhan 430071,China [2]School of Mathematical Sciences,Qufu Normal University,Shandong 273165,China

出　　处：《Acta Mathematica Scientia》2022年第2期551-560,共10页数学物理学报（B辑英文版）

基　　金：supported by NSFC(11931012,11871387,11471187)。

摘　　要：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.

关 键 词：Bi-harmonic sign-changing solution Fountain theorem 

分 类 号：O175[理学—数学]