具有一般奇异项基尔霍夫型方程解的存在性

doi:10.13371/j.cnki.chin.q.j.m.2024.03.009

数学季刊 ›› 2024, Vol. 39 ›› Issue (3): 315-323.doi: 10.13371/j.cnki.chin.q.j.m.2024.03.009

具有一般奇异项基尔霍夫型方程解的存在性

Department of Mathematics, Henan University of Technology, Zhengzhou 450001, China

收稿日期:2023-10-09 出版日期:2024-09-30 发布日期:2024-09-30
通讯作者: SUN Da-wei (1983-), male, native of Kaifeng, Henan, associate professor of Henan University of Technology, engages in nonlinear analysis. E-mail:sundawei16@163.com
作者简介:WANG Ji-nan (1999-), male, native of Zhumadian, Henan, master student of Henan University of Technology, engages in nonlinear functional analysis; SUN Da-wei (1983-), male, native of Kaifeng, Henan, associate professor of Henan University of Technology, engages in nonlinear analysis.

The Existence of Solutions for Kirchhoff-Type Equations with General Singular Terms

Department of Mathematics, Henan University of Technology, Zhengzhou 450001, China

Received:2023-10-09 Online:2024-09-30 Published:2024-09-30
Contact: SUN Da-wei (1983-), male, native of Kaifeng, Henan, associate professor of Henan University of Technology, engages in nonlinear analysis. E-mail:sundawei16@163.com
About author:WANG Ji-nan (1999-), male, native of Zhumadian, Henan, master student of Henan University of Technology, engages in nonlinear functional analysis; SUN Da-wei (1983-), male, native of Kaifeng, Henan, associate professor of Henan University of Technology, engages in nonlinear analysis.

摘要/Abstract

摘要： We study the existence of solutions for Kirchhoff-type equations. Firstly, we use the Sobolev inequality and the weakly lower semi-continuity of the norm to prove that the corresponding function can reach the global minimum. Then, we use the variational method and some analytical techniques to obtain the existence of the positive solution of the equation when λ is small enough.

关键词: Kirchhoff-type equation, The existence, Positive solution, Variational method

Abstract: We study the existence of solutions for Kirchhoff-type equations. Firstly, we use the Sobolev inequality and the weakly lower semi-continuity of the norm to prove that the corresponding function can reach the global minimum. Then, we use the variational method and some analytical techniques to obtain the existence of the positive solution of the equation when λ is small enough.

Key words: Kirchhoff-type equation, The existence, Positive solution, Variational method

王继楠, 孙大为. 具有一般奇异项基尔霍夫型方程解的存在性 [J]. 数学季刊, 2024, 39(3): 315-323.

WANG Ji-nan, SUN Da-wei. The Existence of Solutions for Kirchhoff-Type Equations with General Singular Terms[J]. Chinese Quarterly Journal of Mathematics, 2024, 39(3): 315-323.

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具有一般奇异项基尔霍夫型方程解的存在性

The Existence of Solutions for Kirchhoff-Type Equations with General Singular Terms

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