Opuscula Math. 40, no. 3 (2020), 313-322
https://doi.org/10.7494/OpMath.2020.40.3.313

Opuscula Mathematica

# A unique weak solution for a kind of coupled system of fractional Schrödinger equations

Fatemeh Abdolrazaghi
Abdolrahman Razani

Abstract. In this paper, we prove the existence of a unique weak solution for a class of fractional systems of Schrödinger equations by using the Minty-Browder theorem in the Cartesian space. To this aim, we need to impose some growth conditions to control the source functions with respect to dependent variables.

Keywords: fractional Laplacian, uniqueness, weak solution, nonlinear systems.

Mathematics Subject Classification: 34A08, 35J10, 35D30, 93C15.

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• Fatemeh Abdolrazaghi
• https://orcid.org/0000-0002-3321-9450
• Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, P.O. Box 34149-16818, Qazvin, Iran
• Abdolrahman Razani (corresponding author)
• https://orcid.org/0000-0002-3092-3530
• Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, P.O. Box 34149-16818, Qazvin, Iran
• Communicated by Patrizia Pucci.
• Revised: 2020-02-11.
• Accepted: 2020-02-12.
• Published online: 2020-04-04.