A class of elliptic problems driven by a mixed local-nonlocal operator

IF 0.6 4区数学 Q3 MATHEMATICS

Complex Variables and Elliptic Equations Pub Date : 2023-10-13 DOI:10.1080/17476933.2023.2266689

Zijian Wu, Haibo Chen

引用次数: 0

Abstract

AbstractIn this paper, we consider a class of elliptic problems driven by a mixed local-nonlocal operator. By estimating the critical groups and using Morse theory, the existence of nontrivial solutions is obtained in different cases. Our results extend some classical theorems for semilinear elliptic equations to the mixed local-nonlocal setting.Keywords: Nontrivial solutionssemilinear elliptic problemscritical groupsMorse theoryAMS Subject Classifications: 35J6035J91 AcknowledgementThe authors are grateful to the anonymous referees for their useful comments and suggestions.Disclosure statementNo potential conflict of interest was reported by the author(s).Data availability statementDate sharing is not applicable to this article as no new data were created or analysed in this study.

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一类由混合局部-非局部算子驱动的椭圆型问题

摘要考虑一类由混合局部-非局部算子驱动的椭圆型问题。通过对临界群的估计，利用Morse理论，得到了不同情况下非平凡解的存在性。我们的结果将半线性椭圆方程的一些经典定理推广到局部-非局部混合情况。关键词:非平凡解;半线性椭圆问题;临界群;smorse理论;ams学科分类:35J6035J91致谢感谢匿名审稿人提出的宝贵意见和建议。披露声明作者未报告潜在的利益冲突。数据可用性声明数据共享不适用于本文，因为本研究没有创建或分析新的数据。

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

Complex Variables and Elliptic Equations MATHEMATICS-

CiteScore

2.00

自引率

11.10%

发文量

审稿时长

6-12 weeks

期刊介绍： Complex Variables and Elliptic Equations is devoted to complex variables and elliptic equations including linear and nonlinear equations and systems, function theoretical methods and applications, functional analytic, topological and variational methods, spectral theory, sub-elliptic and hypoelliptic equations, multivariable complex analysis and analysis on Lie groups, homogeneous spaces and CR-manifolds. The Journal was formally published as Complex Variables Theory and Application.