有界域上具有Kirchhoff型扰动的临界Choquard方程

IF 1.1 4区数学 Q2 MATHEMATICS, APPLIED

Applicable Analysis Pub Date : 2023-10-19 DOI:10.1080/00036811.2023.2271945

Xueliang Duan, Xiaofan Wu, Gongming Wei, Haitao Yang

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引用次数: 0

摘要

摘要本文讨论有界域上具有Kirchhoff型扰动的临界Choquard方程{−(1+b‖u‖2)Δu=(∫Ωu2(y)|x−y|4dy)u+λuinΩ，u=0on∂Ω，其中Ω∧RN(N≥5)是光滑有界域，‖⋅‖是H01(Ω)的标准范数。在常数b≥0的适当假设下，在Ω上证明了00是−Δ的第一特征值的解的存在性。此外，我们还证明了λ>λ1和b>0在适当区间内解的多重性。关键词:Choquard方程;kirchhoff问题;临界指数;nehari流形存在性;;;;;本研究得到河南省高等学校重点科研项目[批准号:23A110018]的支持。

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The critical Choquard equations with a Kirchhoff type perturbation in bounded domains

AbstractThis paper deals with the following critical Choquard equation with a Kirchhoff type perturbation in bounded domains, {−(1+b‖u‖2)Δu=(∫Ωu2(y)|x−y|4dy)u+λuinΩ,u=0on∂Ω,where Ω⊂RN(N≥5) is a smooth bounded domain and ‖⋅‖ is the standard norm of H01(Ω). Under the suitable assumptions on the constant b≥0, we prove the existence of solutions for 0<λ≤λ1, where λ1>0 is the first eigenvalue of −Δ on Ω. Moreover, we prove the multiplicity of solutions for λ>λ1 and b>0 in suitable intervals.Keywords: Choquard equationKirchhoff problemcritical exponentNehari manifoldexistenceMathematic Subject classifications: 35A1535J60 Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis research is supported by Key Scientific Research Projects of Colleges and Universities in Henan Province [grant number 23A110018].

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来源期刊

Applicable Analysis 数学-应用数学

CiteScore

2.60

自引率

9.10%

发文量

175

审稿时长

2 months

期刊介绍： Applicable Analysis is concerned primarily with analysis that has application to scientific and engineering problems. Papers should indicate clearly an application of the mathematics involved. On the other hand, papers that are primarily concerned with modeling rather than analysis are outside the scope of the journal General areas of analysis that are welcomed contain the areas of differential equations, with emphasis on PDEs, and integral equations, nonlinear analysis, applied functional analysis, theoretical numerical analysis and approximation theory. Areas of application, for instance, include the use of homogenization theory for electromagnetic phenomena, acoustic vibrations and other problems with multiple space and time scales, inverse problems for medical imaging and geophysics, variational methods for moving boundary problems, convex analysis for theoretical mechanics and analytical methods for spatial bio-mathematical models.