具有一般奇异项基尔霍夫型方程解的存在性&nbsp;

王继楠, 孙大为

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

数学季刊 >

2024 , Vol. 39 >Issue 3: 315 - 323

DOI: https://doi.org/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

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

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.

收稿日期: 2023-10-09

网络出版日期: 2024-09-30

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

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

Received date: 2023-10-09

Online published: 2024-09-30

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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

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

Abstract

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

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