Positive solutions of fractional Schrödinger-Poisson systems involving critical nonlinearities with potential

Authors

Haining Fan
Zhaosheng Feng, The University of Texas Rio Grande Valley
Xingjie Yan

Document Type

Article

Publication Date

2-2022

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

Comments

Copyright © 2022 Khayyam Publishing, Inc.

Recommended Citation

Fan, Haining, Zhaoshengn Feng, and Xingjie Yan. "Positive solutions of fractional Schrödinger-Poisson systems involving critical nonlinearities with potential." Differential and Integral Equations 35, no. 1/2 (2022): 1-56. https://doi.org/10.57262/die035-0102-1

Publication Title

Differential Integral Equations

DOI

10.57262/die035-0102-1