Existence and Multiplicity of Solutions for a Class of Kirchhoff–Boussinesq-Type Problems with Logarithmic Growth

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-05-02 DOI:10.1007/s00009-024-02649-6

Romulo D. Carlos, Lamine Mbarki, Shuang Yang

引用次数: 0

Abstract

In this paper, two problems related to the following class of elliptic Kirchhoff–Boussinesq-type models are analyzed in the subcritical ($\beta =0$) and critical ($\beta =1$) cases:

$$\begin{aligned} \Delta ^{2} u \!- \!\Delta _p u \!=\! \tau |u|^{q-2} u{\ln |u|}\!+\!\beta |u|^{2_{**}-2}u\ \text{ in } \ \Omega \ \ \text{ and } \ {\Delta u=u=0} \ \text{ on } \ \ \partial \Omega , \end{aligned}$$

where $\tau >0$, $2< p< 2^{*}= \frac{2N}{N-2}$ for $ N\ge 3$ and $2_{**}= \infty $ for $N=3$, $N=4$, $2_{**}= \frac{2N}{N-4}$ for $N\ge 5$. The first one is concerned with the existence of a nontrivial ground-state solution via variational methods. As for the second problem, we prove the multiplicity of such a solution using the Mountain Pass Theorem.

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具有对数增长的一类基尔霍夫-布西内斯克问题的解的存在性和多重性

本文在次临界（（beta =0））和临界（（beta =1））情况下分析了与以下一类椭圆基尔霍夫-布西尼斯克（Kirchhoff-Boussinesq）型模型相关的两个问题：$$\begin{aligned} u \!\Delta ^{2} u \！-\！\Delta _p u \！=\！\tau |u|^{q-2} u{ln |u|}\! +\!\ （Omega）（text{ and }\ {Delta u=u=0}\ on }\ \partial\Omega , \end{aligned}$where$\tau >0$,$2< p<；2^{*}= \frac{2N}{N-2}$ for $ N\ge 3$ and $2_{**}= \infty $ for $N=3$, $N=4$, $2_{**}= \frac{2N}{N-4}$ for $N\ge 5$.第一个问题是关于通过变分法存在一个非小的基态解。至于第二个问题，我们利用山口定理证明了这种解的多重性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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