The existence and multiplicity of solutions of Kirchhoff type linearly coupled systems with critical exponents

Xiaofan Wu; Xueliang Duan; Qingquan Yang; Xiaofan Wu; Xueliang Duan; Qingquan Yang

doi:10.3934/math.2026039

AIMS Mathematics

2026, Volume 11, Issue 1: 907-914. doi: 10.3934/math.2026039

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Research article

The existence and multiplicity of solutions of Kirchhoff type linearly coupled systems with critical exponents

School of Mathematics and Statistics, Zhengzhou Normal University, Zhengzhou, Henan 450044, China

Received: 01 December 2025 Revised: 04 January 2026 Accepted: 08 January 2026 Published: 13 January 2026
MSC : 35J20, 35J60

We consider the critical problems of Kirchhoff type linearly coupled systems. In applying variational methods, we establish both the existence and multiplicity of solutions in the four-dimensional case.
- Kirchhoff equation,
- linearly coupled system,
- Sobolev critical exponent,
- variational method
Citation: Xiaofan Wu, Xueliang Duan, Qingquan Yang. The existence and multiplicity of solutions of Kirchhoff type linearly coupled systems with critical exponents[J]. AIMS Mathematics, 2026, 11(1): 907-914. doi: 10.3934/math.2026039

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Abstract

We consider the critical problems of Kirchhoff type linearly coupled systems. In applying variational methods, we establish both the existence and multiplicity of solutions in the four-dimensional case.

References

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