Multiple positive solutions for a class of Kirchhoff equation on bounded domain. Issue 15 (13th October 2022)

• Record Type: Journal Article
• Authors: Cai, Li; Zhang, Fubao
• Is Part Of: Applicable analysis. Volume 101:Issue 15(2022)
• Page Start: 5273
• Page End: 5288
• Publication Date: 2022-10-13
• Subjects: Kirchhoff equation -- Lusternik–Schnirelmann theory; 35J47 -- 35J50; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2021.1889520
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: In this paper, we study the existence of multiple positive solutions of the following Kirchhoff equation 1 { − ( a + b ∫ Ω | ∇ u | 2 d x ) Δ u + λ u = | u | p ϵ − 2 u, in Ω, u = 0, in R 3 ∖ Ω, u > 0, in Ω, where ϵ > 0, Ω is a regular bounded domain of R 3, λ ≥ 0, a, b > 0, p ϵ := 6 − ϵ > 4. We obtain the existence of c a t Ω ( Ω ) + 1 positive solutions by using the variational methods and Lusternik–Schnirelmann theory.