GROUND STATES FOR A FRACTIONAL REACTION-DIFFUSION SYSTEM

Peng Chen; Zhijie Cao; Sitong Chen; Xianhua Tang

doi:10.11948/20200349

2021 Volume 11 Issue 1

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Peng Chen, Zhijie Cao, Sitong Chen, Xianhua Tang. GROUND STATES FOR A FRACTIONAL REACTION-DIFFUSION SYSTEM[J]. Journal of Applied Analysis & Computation, 2021, 11(1): 556-567. doi: 10.11948/20200349

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Peng Chen, Zhijie Cao, Sitong Chen, Xianhua Tang. GROUND STATES FOR A FRACTIONAL REACTION-DIFFUSION SYSTEM[J]. Journal of Applied Analysis & Computation, 2021, 11(1): 556-567. doi: 10.11948/20200349

GROUND STATES FOR A FRACTIONAL REACTION-DIFFUSION SYSTEM

1.
College of Science, China Three Gorges University, Yichang, Hubei 443002, China
2.
School of Mathematics and Statistics, Central South University, Changsha, Hunan 410083, China

Corresponding author: Email: pengchen729@sina.com(P. Chen)

Abstract

Abstract

In this paper, we prove the existence of the ground state of a strongly indefinite fractional reaction-diffusion system based on the Non-Nehari method established by Tang-Chen-Lin-Yu [J. Differ. Equ., 2020(268), 4663-4690]. In particular, neither any monotonicity condition nor any Ambrosetti-Rabinowitz growth condition is required. To our knowledge, this is the first result about the ground states with the strongly indefinite case for fractional reaction-diffusion system.
- Reaction-diffusion system /
- ground states /
- strongly indefinite functional
MSC: 37J45, 58E05, 70H05

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References

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