数学
对数
简并能级
索波列夫空间
紧凑空间
单调函数
数学分析
摄动(天文学)
山口
山口定理
指数
类型(生物学)
临界指数
非线性系统
纯数学
缩放比例
物理
几何学
量子力学
语言学
哲学
生态学
生物
标识
DOI:10.1080/17476933.2023.2298838
摘要
In this paper, the following Kirchhoff type elliptic equation −(a+b∫Ω|∇u|2dx)Δu=λ|u|q−2uln|u|2+|u|4u, which involves a power type nonlinearity with critical Sobolev exponent and a logarithmic type perturbation, is investigated. The fact that the logarithmic term satisfies neither the monotonicity condition nor the Ambrosetti-Rabinowitz condition brings some additional difficulties when one is looking for weak solutions to this problem. By the use of the Mountain Pass Lemma and the concentration compactness principle, it is proved that the problem admits a ground state solution for q∈(4,6) and for any λ>0. It is worth pointing out that the analysis includes both the nondegenerate case (a>0) and the degenerate case (a = 0).
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