Classification of nonnegative solutions to fractional Schrödinger-Hatree-Maxwell type system

Yaqiong Liu; Yunting Li; Qiuping Liao; Yunhui Yi; Yaqiong Liu; Yunting Li; Qiuping Liao; Yunhui Yi

doi:10.3934/math.2021794

AIMS Mathematics

2021, Volume 6, Issue 12: 13665-13688. doi: 10.3934/math.2021794

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Classification of nonnegative solutions to fractional Schrödinger-Hatree-Maxwell type system

School of Mathematics and Computer Science, Jiangxi Science and Technology Normal University, Nanchang 330038, China

Received: 07 July 2021 Accepted: 07 September 2021 Published: 26 September 2021
MSC : 35B08, 35B50, 35J61, 35R11

In this paper, we are concerned with the fractional Schrödinger-Hatree-Maxwell type system. We derive the forms of the nonnegative solution and classify nonlinearities by appling a variant (for nonlocal nonlinearity) of the direct moving spheres method for fractional Laplacians. The main ingredients are the variants (for nonlocal nonlinearity) of the maximum principles, i.e., narrow region principle (Theorem 2.3).
- fractional Laplacians,
- nonnegative solutions,
- nonlocal nonlinearities,
- direct method of moving spheres
Citation: Yaqiong Liu, Yunting Li, Qiuping Liao, Yunhui Yi. Classification of nonnegative solutions to fractional Schrödinger-Hatree-Maxwell type system[J]. AIMS Mathematics, 2021, 6(12): 13665-13688. doi: 10.3934/math.2021794

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Abstract

In this paper, we are concerned with the fractional Schrödinger-Hatree-Maxwell type system. We derive the forms of the nonnegative solution and classify nonlinearities by appling a variant (for nonlocal nonlinearity) of the direct moving spheres method for fractional Laplacians. The main ingredients are the variants (for nonlocal nonlinearity) of the maximum principles, i.e., narrow region principle (Theorem 2.3).

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