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

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

Chinese Quarterly Journal of Mathematics ›› 2024, Vol. 39 ›› Issue (3): 315-323.doi: 10.13371/j.cnki.chin.q.j.m.2024.03.009

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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.

Abstract

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

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

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