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January/February 2022 Positive solutions of fractional Schrödinger-Poisson systems involving critical nonlinearities with potential
Haining Fan, Zhaoshengn Feng, Xingjie Yan
Differential Integral Equations 35(1/2): 1-56 (January/February 2022).

Abstract

In this paper, we study the existence of multiple positive solutions for a class of fractional Schrödinger-Poisson systems involving sign-changing potential and critical nonlinearities on an unbounded domain. By means of the Nehari manifold and Ljusternik-Schnirelmann category, we show how the coefficient $g(x)$ of the critical nonlinearity affects the number of positive solutions, and present a novel relationship between the number of positive solutions and the category of the global maximum set of $g(x)$. The new feature which distinguishes this paper from other related works lies in the fact that we focus on the case of $1 < q < 2$, which has not been presented in the literature.

Citation

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Haining Fan. Zhaoshengn Feng. Xingjie Yan. "Positive solutions of fractional Schrödinger-Poisson systems involving critical nonlinearities with potential." Differential Integral Equations 35 (1/2) 1 - 56, January/February 2022.

Information

Published: January/February 2022
First available in Project Euclid: 6 January 2022

Subjects:
Primary: 35A15 , 35B09 , 35B33 , 35J05

Rights: Copyright © 2022 Khayyam Publishing, Inc.

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Vol.35 • No. 1/2 • January/February 2022
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