Multiplicity results for solutions of p-biharmonic problems

Yao Lu; Yongqiang Fu

doi:10.1016/j.na.2019.111596

Multiplicity results for solutions of p-biharmonic problems

Yao Lu
, Yongqiang Fu^*

^*Corresponding author for this work

School of Mathematics

Harbin Institute of Technology

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

In this paper, we deal with the multiplicity existence of solutions for the following p-biharmonic equation: Δ_p ²u=λ|u|^p−2u+|u|^q−2u,inΩ,u=Δu=0,on∂Ω,where Ω is a bounded domain in R^N, Δ_p ²u=Δ(|Δu|^p−2Δu), [Formula presented], λ∈R is a parameter. When p<q<p^∗, we prove that the above problem possesses infinitely many solutions. While when q=p^∗, a multiplicity existence result is obtained.

Original language	English
Article number	111596
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	190
DOIs	https://doi.org/10.1016/j.na.2019.111596
State	Published - Jan 2020

Keywords

Cohomological linking
Critical nonlinearity
Fountain theorem over cones
p-biharmonic operator

Access to Document

10.1016/j.na.2019.111596

Cite this

@article{71c157568b6b4f72832da70a8618b628,

title = "Multiplicity results for solutions of p-biharmonic problems",

abstract = "In this paper, we deal with the multiplicity existence of solutions for the following p-biharmonic equation: Δp 2u=λ|u|p−2u+|u|q−2u,inΩ,u=Δu=0,on∂Ω,where Ω is a bounded domain in RN, Δp 2u=Δ(|Δu|p−2Δu), [Formula presented], λ∈R is a parameter. When p∗, we prove that the above problem possesses infinitely many solutions. While when q=p∗, a multiplicity existence result is obtained.",

keywords = "Cohomological linking, Critical nonlinearity, Fountain theorem over cones, p-biharmonic operator",

author = "Yao Lu and Yongqiang Fu",

note = "Publisher Copyright: {\textcopyright} 2019 Elsevier Ltd",

year = "2020",

month = jan,

doi = "10.1016/j.na.2019.111596",

language = "英语",

volume = "190",

journal = "Nonlinear Analysis, Theory, Methods and Applications",

issn = "0362-546X",

publisher = "Elsevier Ltd",

}

TY - JOUR

T1 - Multiplicity results for solutions of p-biharmonic problems

AU - Lu, Yao

AU - Fu, Yongqiang

PY - 2020/1

Y1 - 2020/1

N2 - In this paper, we deal with the multiplicity existence of solutions for the following p-biharmonic equation: Δp 2u=λ|u|p−2u+|u|q−2u,inΩ,u=Δu=0,on∂Ω,where Ω is a bounded domain in RN, Δp 2u=Δ(|Δu|p−2Δu), [Formula presented], λ∈R is a parameter. When p∗, we prove that the above problem possesses infinitely many solutions. While when q=p∗, a multiplicity existence result is obtained.

AB - In this paper, we deal with the multiplicity existence of solutions for the following p-biharmonic equation: Δp 2u=λ|u|p−2u+|u|q−2u,inΩ,u=Δu=0,on∂Ω,where Ω is a bounded domain in RN, Δp 2u=Δ(|Δu|p−2Δu), [Formula presented], λ∈R is a parameter. When p∗, we prove that the above problem possesses infinitely many solutions. While when q=p∗, a multiplicity existence result is obtained.

KW - Cohomological linking

KW - Critical nonlinearity

KW - Fountain theorem over cones

KW - p-biharmonic operator

UR - https://www.scopus.com/pages/publications/85072182106

U2 - 10.1016/j.na.2019.111596

DO - 10.1016/j.na.2019.111596

M3 - 文章

AN - SCOPUS:85072182106

SN - 0362-546X

VL - 190

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

M1 - 111596

ER -

Multiplicity results for solutions of p-biharmonic problems

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this