一类具有临界增长和临界频率的p(x)- kirchhoff型方程的存在性结果

IF 0.5 4区数学 Q3 MATHEMATICS

Journal of Mathematical Physics Analysis Geometry Pub Date : 2023-04-01 DOI:10.1063/5.0133793

Rui He, Sihua Liang

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引用次数: 0

摘要

本文研究一类具有临界增长和临界频率的p(x)-拉普拉斯方程。利用变分方法和一些分析技巧，得到了该问题非平凡解的存在性和多重性。本文的新颖之处在于两个方面:(1)该方程包含退化情况，对应于Kirchhoff项K在零处消失;(2)我们的论文是关于临界项的出现，可以看作是Zhang等人的结果的部分推广。j .不同。方程2018,1-20]关于该问题在亚临界情况下解的存在性。

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Existence results for a class of p(x)-Kirchhoff-type equations with critical growth and critical frequency

This article deals with a class of p(x)-Laplace equations with critical growth and critical frequency. By using the variational methods and some analytical skills, we obtain the existence and multiplicity of nontrivial solutions for this problem. The novelty of this paper lies in two aspects: (1) this equation contains the degenerate case, which corresponds to the Kirchhoff term K vanishing at zero and (2) our paper is about the appearance of critical terms, which can be viewed as a partial extension of the results of Zhang et al. [Electron. J. Differ. Equations 2018, 1–20] concerning the existence of solutions to this problem in the subcritical case.

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来源期刊

Journal of Mathematical Physics Analysis Geometry PHYSICS, MATHEMATICAL-

CiteScore

0.70

自引率

20.00%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Mathematical Physics, Analysis, Geometry (JMPAG) publishes original papers and reviews on the main subjects: mathematical problems of modern physics; complex analysis and its applications; asymptotic problems of differential equations; spectral theory including inverse problems and their applications; geometry in large and differential geometry; functional analysis, theory of representations, and operator algebras including ergodic theory. The Journal aims at a broad readership of actively involved in scientific research and/or teaching at all levels scientists.