The existence and nonexistence of positive solutions for a singular Kirchhoff equation with convection term

Xiaohui Qiu; Baoqiang Yan; Xiaohui Qiu; Baoqiang Yan

doi:10.3934/mbe.2022494

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 10: 10581-10601. doi: 10.3934/mbe.2022494

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The existence and nonexistence of positive solutions for a singular Kirchhoff equation with convection term

Xiaohui Qiu ,
Baoqiang Yan ^,

School of Mathematical Sciences, Shandong Normal University, Jinan 250000, China

Received: 26 June 2022 Revised: 13 July 2022 Accepted: 18 July 2022 Published: 25 July 2022

This paper considers a singular Kirchhoff equation with convection and a parameter. By defining new sub-supersolutions, we prove a new sub-supersolution theorem. Combining method of sub-supersolution with the comparison principle, for Kirchhoff equation with convection, we get the conclusion about positive solutions when nonlinear term is singular and sign-changing.
- a singular Kirchhoff equation,
- nonlinear term,
- positive solution,
- sub-supersolution,
- the comparison principle
Citation: Xiaohui Qiu, Baoqiang Yan. The existence and nonexistence of positive solutions for a singular Kirchhoff equation with convection term[J]. Mathematical Biosciences and Engineering, 2022, 19(10): 10581-10601. doi: 10.3934/mbe.2022494

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Abstract

This paper considers a singular Kirchhoff equation with convection and a parameter. By defining new sub-supersolutions, we prove a new sub-supersolution theorem. Combining method of sub-supersolution with the comparison principle, for Kirchhoff equation with convection, we get the conclusion about positive solutions when nonlinear term is singular and sign-changing.

References

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