Positive solutions for the fractional Schrödinger equations with logarithmic and critical non-linearities

Authors

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

Document Type

Article

Publication Date

7-21-2021

Abstract

In this paper, we study a class of fractional Schrödinger equations involving logarithmic and critical non-linearities on an unbounded domain, and show that such an equation with positive or sign-changing weight potentials admits at least one positive ground state solution and the associated energy is positive (or negative). By applying the Nehari manifold method and Ljusternik–Schnirelmann category, we investigate how the weight potential affects the multiplicity of positive solutions, and obtain the relationship between the number of positive solutions and the category of some sets related to the weight potential.

Recommended Citation

Fan, H., Feng, Z. and Yan, X. (2021), Positive solutions for the fractional Schrödinger equations with logarithmic and critical non-linearities. Trans. London Math. Soc., 8: 206-242. https://doi.org/10.1112/tlm3.12034

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Publication Title

Trans. London Math. Soc.

DOI

10.1112/tlm3.12034