The nontrivial solutions for nonlinear fractional Schrödinger-Poisson system involving new fractional operator

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Original research article

Author(s):

Hamza Boutebba, Hakim Lakhal, Kamel Slimani, Tahar Belhadi

Laboratory of Applied Mathematics and History and Didactics of Mathematics (LAMAHIS), Department of Mathematics, University of 20 August 1955, P.O. Box 26 – 21000, Skikda, Algeria.

Advances in the Theory of Nonlinear Analysis and its Applications 7(1), 121-132.

Received: July 5, 2022

Accepted: December 2, 2022

Published: December 5, 2022

Abstract

In this paper, we investigate the existence of nontrivial solutions in the Bessel potential space for nonlinear fractional Schrödinger–Poisson systems involving distributional Riesz fractional derivatives. By using the mountain pass theorem in combination with the perturbation method, we prove the existence of solutions.

Keywords: Fractional Schrödinger–Poisson system, mountain pass theorem, Bessel potential space, perturbation method.

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APA Style

Hamza, B., Lakhal, H., Kamel, S., & Tahar, B. (2023). The nontrivial solutions for nonlinear fractional Schrödinger-Poisson system involving new fractional operator. Advances in the Theory of Nonlinear Analysis and its Application , 7 (1), 121-132.