Existence for critical Schrödinger–Bopp–Podolsky system with $ p $-Laplacian in $ \mathbb{R}^3 $

Liteng Liu; Deli Zhang; Yueqiang Song; Liteng Liu; Deli Zhang; Yueqiang Song

doi:10.3934/era.2026065

Electronic Research Archive

2026, Volume 34, Issue 3: 1434-1447. doi: 10.3934/era.2026065

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Existence for critical Schrödinger–Bopp–Podolsky system with $ p $-Laplacian in $ \mathbb{R}^3 $

College of Mathematics, Changchun Normal University, Changchun 130032, China

Received: 08 December 2025 Revised: 06 February 2026 Accepted: 09 February 2026 Published: 11 February 2026

We intend to study a class of the critical Schrödinger–Bopp–Podolsky system with $ p $-Laplacian in $ \mathbb{R}^3 $. Under different perturbation terms, the existence and multiplicity of nontrivial solutions are obtained by using critical point theorem. Considering the influence of the $ p $-Laplacian operator and critical and nonlocal terms, which cause the loss of the compactness condition, we attempt to address this difficulty by using the concentration-compactness principle and some clever analysis.
- Schrödinger–Bopp–Podolsky system,
- critical growth,
- $ p $-Laplacian,
- choquard nonlinearity,
- variational methods,
- concentration-compactness principles
Citation: Liteng Liu, Deli Zhang, Yueqiang Song. Existence for critical Schrödinger–Bopp–Podolsky system with $ p $-Laplacian in $ \mathbb{R}^3 $[J]. Electronic Research Archive, 2026, 34(3): 1434-1447. doi: 10.3934/era.2026065

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Abstract

We intend to study a class of the critical Schrödinger–Bopp–Podolsky system with $ p $-Laplacian in $ \mathbb{R}^3 $. Under different perturbation terms, the existence and multiplicity of nontrivial solutions are obtained by using critical point theorem. Considering the influence of the $ p $-Laplacian operator and critical and nonlocal terms, which cause the loss of the compactness condition, we attempt to address this difficulty by using the concentration-compactness principle and some clever analysis.

References

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