Existence and multiplicity results for the fractional Schrödinger equations with indefinite potentials

This paper is concerned with the following nonlinear fractional Schrödinger equation with a magnetic field: [Formula: see text] where ɛ > 0 is a parameter, s ∈ (0, 1), N ≥ 3, [Formula: see text] and [Formula: see text] are continuous potentials, and V may be sign-changing; the nonlinearity is superlinear with subcritical growth but without satisfying the Ambrosetti–Rabinowitz condition. Based on the Nehari manifold method, concentration-compactness principle, and variational methods, we prove the existence of a ground state solution for the above equation when ɛ is sufficiently small. Our results improve and extend the result of Ambrosio and d’Avenia [J. Differ. Equations 264, 3336–3368 (2018)].

show abstract

Some new asymptotic properties on solutions to fractional evolution equations in Banach spaces

Chang

Zhao

2021

Applicable Analysis

View full text Add to dashboard Cite

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Existence and multiplicity results for the fractional Schrödinger equations with indefinite potentials

Cited by 7 publications

References 27 publications

The Effect of the Domain Topology on the Number of Positive Solutions for Fractional p-laplacian Equation with Critical Growth

The Effect of the Domain Topology on the Number of Positive Solutions for Fractional p-laplacian Equation with Critical Growth

Ground state solution for a nonlinear fractional magnetic Schrödinger equation with indefinite potential

Some new asymptotic properties on solutions to fractional evolution equations in Banach spaces

Contact Info

Product

Resources

About