Multiplicity results for solutions of p-biharmonic problems. (January 2020)

• Record Type: Journal Article
• Authors: Lu, Yao; Fu, Yongqiang
• Is Part Of: Nonlinear analysis. Volume 190(2020)
• Publication Date: 2020-01
• Subjects: 35R11 -- 35A15 -- 45K05; p-biharmonic operator -- Cohomological linking -- Fountain theorem over cones -- Critical nonlinearity; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.111596
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we deal with the multiplicity existence of solutions for the following p -biharmonic equation: Δ p 2 u = λ | u | p − 2 u + | u | q − 2 u, in Ω, u = Δ u = 0, on ∂ Ω, where Ω is a bounded domain in R N, Δ p 2 u = Δ ( | Δ u | p − 2 Δ u ), p < q ≤ p ∗ = N p N − 2 p, 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.