Existence and non-existence results for some weighted fourth-order elliptic equations

Zongming Guo; Fangshu Wan; Liping Wang

doi:10.1142/S0219199725500397

Existence and non-existence results for some weighted fourth-order elliptic equations

Zongming Guo, Fangshu Wan, Liping Wang^*

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

New types of Caffarelli–Kohn–Nirenberg inequalities and Rellich inequality are established in some weighted Hilbert spaces. Using such inequalities, we study existence and qualitative properties of positive solutions for weighted fourth-order elliptic equations with singular potential. We also present Liouville-type results for the equations.

Original language	English
Article number	2550039
Journal	Communications in Contemporary Mathematics
DOIs	https://doi.org/10.1142/S0219199725500397
State	Accepted/In press - 2025

Keywords

Caffarelli–Kohn–Nirenberg inequalities
Liouville-type results
positive solutions
Rellich inequalities
weighted fourth-order elliptic equations

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10.1142/S0219199725500397

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title = "Existence and non-existence results for some weighted fourth-order elliptic equations",

abstract = "New types of Caffarelli–Kohn–Nirenberg inequalities and Rellich inequality are established in some weighted Hilbert spaces. Using such inequalities, we study existence and qualitative properties of positive solutions for weighted fourth-order elliptic equations with singular potential. We also present Liouville-type results for the equations.",

keywords = "Caffarelli–Kohn–Nirenberg inequalities, Liouville-type results, positive solutions, Rellich inequalities, weighted fourth-order elliptic equations",

author = "Zongming Guo and Fangshu Wan and Liping Wang",

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year = "2025",

doi = "10.1142/S0219199725500397",

language = "英语",

journal = "Communications in Contemporary Mathematics",

issn = "0219-1997",

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T1 - Existence and non-existence results for some weighted fourth-order elliptic equations

AU - Guo, Zongming

AU - Wan, Fangshu

AU - Wang, Liping

N1 - Publisher Copyright: © World Scientific Publishing Company.

PY - 2025

Y1 - 2025

N2 - New types of Caffarelli–Kohn–Nirenberg inequalities and Rellich inequality are established in some weighted Hilbert spaces. Using such inequalities, we study existence and qualitative properties of positive solutions for weighted fourth-order elliptic equations with singular potential. We also present Liouville-type results for the equations.

AB - New types of Caffarelli–Kohn–Nirenberg inequalities and Rellich inequality are established in some weighted Hilbert spaces. Using such inequalities, we study existence and qualitative properties of positive solutions for weighted fourth-order elliptic equations with singular potential. We also present Liouville-type results for the equations.

KW - Caffarelli–Kohn–Nirenberg inequalities

KW - Liouville-type results

KW - positive solutions

KW - Rellich inequalities

KW - weighted fourth-order elliptic equations

UR - https://www.scopus.com/pages/publications/105003465219

U2 - 10.1142/S0219199725500397

DO - 10.1142/S0219199725500397

M3 - 文章

AN - SCOPUS:105003465219

SN - 0219-1997

JO - Communications in Contemporary Mathematics

JF - Communications in Contemporary Mathematics

M1 - 2550039

ER -

Existence and non-existence results for some weighted fourth-order elliptic equations

Abstract

Keywords

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