Publication Cover
Applicable Analysis
An International Journal
Volume 100, 2021 - Issue 6
347
Views
6
CrossRef citations to date
0
Altmetric
Articles

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

&
Pages 1198-1212 | Received 20 Apr 2019, Accepted 21 Jun 2019, Published online: 03 Jul 2019
 

ABSTRACT

In this paper, we consider the fractional Schrödinger equations (Δ)su+V(x)u=f(x,u)in RN, where s ∈ (0,1) and N>2s. Firstly, we prove that the problem admits a nontrivial solution and infinitely many nontrivial solutions under the assumptions that V is allowed to be indefinite potential and f is superlinear and subcritical. In addition, we establish an existence criterion of infinitely many nontrivial solutions for the aforementioned problem with concave and critical nonlinearities as well as indefinite potential, which improves the result of Du and Tian [Infinitely many solutions of the nonlinear fractional Schrödinger equations. Discrete Contin Dyn Syst B. 2016;21(10):3407–3428 (Theorem 1.6)].

AMS SUBJECT CLASSIFICATION (2010):

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research is supported in part by the National Natural Science Foundation of China (NSF) of China (11671181).

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.