Existence and multiplicity of solutions to $ p $-Kirchhoff-Choquard-type equations

Bing Long; Yulin Zhao; Bing Long; Yulin Zhao

doi:10.3934/math.2026703

AIMS Mathematics

2026, Volume 11, Issue 6: 17144-17165. doi: 10.3934/math.2026703

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Research article

Existence and multiplicity of solutions to $ p $-Kirchhoff-Choquard-type equations

Bing Long ,
Yulin Zhao ^,

School of Science, Hunan University of Technology, Zhuzhou 412007, Hunan, China

Received: 10 December 2025 Revised: 07 February 2026 Accepted: 25 February 2026 Published: 12 June 2026
MSC : 31A30, 35J60, 35J75

In this paper, we investigate the existence and multiplicity of solutions for a $ p $-Kirchhoff-Choquard-type equation involving a critical exponent. First, we employ the concentration-compactness principle to overcome the lack of compactness arising from the critical exponent. Then, under appropriate assumptions, we obtain the existence of solutions by applying the mountain pass theorem, the symmetric mountain pass theorem, the dual fountain theorem, and various necessary analytical techniques.
- Kirchhoff-Choquard equation,
- critical exponent,
- mountain pass theorem,
- symmetric mountain pass theorem,
- dual fountain theorem
Citation: Bing Long, Yulin Zhao. Existence and multiplicity of solutions to $ p $-Kirchhoff-Choquard-type equations[J]. AIMS Mathematics, 2026, 11(6): 17144-17165. doi: 10.3934/math.2026703

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Abstract

In this paper, we investigate the existence and multiplicity of solutions for a $ p $-Kirchhoff-Choquard-type equation involving a critical exponent. First, we employ the concentration-compactness principle to overcome the lack of compactness arising from the critical exponent. Then, under appropriate assumptions, we obtain the existence of solutions by applying the mountain pass theorem, the symmetric mountain pass theorem, the dual fountain theorem, and various necessary analytical techniques.

References

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