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<p>In this paper, we consider a critical bi-harmonic elliptic equation perturbed by a logarithmic type subcritical term. This problem has been studied by Li et al. in (J Differ Equ 365: 1–37, 2023) and by Zhang et al. in (Appl Math Lett 145:No.108784, 2023], where existence and non-existence of weak solutions were obtained when the domain and the parameters fulfill certain conditions. By combining the symmetric mountain pass lemma with the concentration compactness principle, we show the existence of infinitely many solutions to this problem. A proper truncation on the critical term plays a key role in this process. The result complements some known ones.</p>

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Infinitely many solutions to a critical bi-harmonic elliptic equation with logarithmic type perturbation

  • 期刊论文

  • 发表日期：

    2025年4月24日

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  • Haixia Li

摘要

In this paper, we consider a critical bi-harmonic elliptic equation perturbed by a logarithmic type subcritical term. This problem has been studied by Li et al. in (J Differ Equ 365: 1–37, 2023) and by Zhang et al. in (Appl Math Lett 145:No.108784, 2023], where existence and non-existence of weak solutions were obtained when the domain and the parameters fulfill certain conditions. By combining the symmetric mountain pass lemma with the concentration compactness principle, we show the existence of infinitely many solutions to this problem. A proper truncation on the critical term plays a key role in this process. The result complements some known ones.